Documentation on Limitations and Applicabilities of

Technical Report IRRP-97-4 August 1997

US Army Corps of Engineers Waterways Experiment Station

Installation Restoration Research Program

Documentation on Limitations and Applicabilities of the Use of Off-the-Shelf Groundwater Models in Site Cleanup by

Carlos E. Ruiz, Mansour Zakikhani, Christian J. McGrath, Patrick N. Deliman, Stacy Howington, Robert A. Evans, Fred T. Tracy

Approved For Public Release; Distribution Is Unlimited

$£10 QUALITY INSPECTED g

Prepared for Headquarters, U.S. Army Corps of Engineers

19970916 151

The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. The findings of this report are not to be construed as an official Department of the Army position, unless so designated by other authorized documents.

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Installation Restoration Research Program

Technical Report IRRP-97-4 August 1997

Documentation on Limitations and Applicabilities of the Use of Off-the-Shelf Groundwater Models in Site Cleanup by Carlos E. Ruiz, Mansour Zakikhani, Christian J. McGrath, Patrick N. Deliman, Stacy Howington, Robert A. Evans, Fred T. Tracy U.S. Army Corps of Engineers Waterways Experiment Station 3909 Halls Ferry Road Vicksburg, MS 39180-6199

Final report Approved for public release; distribution is unlimited

Prepared for

U.S. Army Corps of Engineers Washington, DC 20314-1000

US Army Corps of Engineers Waterways Experiment Station

HEA00UABTE8S BWLWHG

ENTRANCE

ENVnONMEKTM. IAB0RATORY

FOR INFORMATION CONTACT: PUBLIC AFFAIRS OFFICE U.S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION 3909 HALLS FERRY ROAD VICKSBURG, MISSISSIPPI 39180-6199 PHONE (601) 634-2502

AREA OF RESERVATION < 2.7saKm

Waterways Experiment Station Cataloging-in-Publication Data Documentation on limitations and applications of the use of off-the-shelf groundwater models in site cleanup / by Carlos E. Ruiz... [et al.]; prepared for U.S. Army Corps of Engineers. 211 p. : ill.; 28 cm. - (Technical report; IRRP-97-4) Includes bibliographic references. 1. Groundwater - Mathematical models ~ Evaluation. 2. Multiphase flow Mathematical models. 3. Two-phase flow-Mathematical models. I. Ruiz, Carlos E. II. United States. Army. Corps of Engineers. III. U.S. Army Engineer Waterways Experiment Station. IV. Installation Restoration Research Program. V. Series: Technical report (U.S. Army Engineer Waterways Experiment Station) ; IRRP-97-4. TA7 W34 no.IRRP-97-4

Contents

Preface

ix

Conversion Factors, Non-SI to SI Units of Measurement

xi

1—Overview

1

2—Literature Review and Model Selection

3

Initial Screening Classifications of Models Groundwater Modeling Saturated Unsaturated Model Selection Model Evaluation, Verification, and Validation 3—Test Cases Overview Saturated Unsaturated Coupled Unsaturated/Saturated Hypothetical Scenarios 4—Models Description Saturated Flow and/or Transport Models MOC MODFLOW MT3D PLASM RANDOM WALK Unsaturated Flow and/or Transport Models UNSAT1 CHEMFLO PRZM-2 Coupled Unsaturated/Saturated Flow and/or Transport Models . FEMWATER LEWASTE SUTRA VS2DT

3 4 5 5 9 15 17 20 20 20 23 25 32 34 34 34 40 45 51 53 62 62 69 74 78 78 82 86 90

in

Multiphase Flow and Transport Models— MOFAT and MOTRANS Input/output parameters Equations Numerical methods Evaluation Documentation examples Synthetic benchmarks Heterogeneous media Summary 5—Model Evaluation Summary MOC MODFLOW MT3D PLASM RANDOM WALK FEMWATER and LEWASTE UNSAT1 CHEMFLOW PRZM-2 SUTRA VS2DT MOFAT and MOTRANS

97 99 100 102 102 103 107 107 107 112 112 113 116 118 119 121 123 124 125 126 127 129

References

131

Appendix A: Abbreviated List of Subsurface Models

Al

Appendix B: Equilibrium Partition Formulations

Bl

SF298

List of Figures Figure 1.

Matric potential expressions and default units

11

Figure 2.

Soil-water retention relationships

12

Figure 3.

Hydraulic conductivity relationships

13

Figure 4.

Two-dimensional transport from a continuous point source—Case 1

22

Experimental soil-water retention curve for Columns 1 and 2

24

Figure 6.

Two-dimensional column grid

25

Figure 7.

Moisture-retention function, van Genuchten model ...

26

Figure 8.

Moisture-retention function, Haverkamp model

26

Figure 5.

IV

Figure 9.

Moisture-retention function, Brooks and Corey model

27

Figure 10. Schematic representation of Vauclin's infiltration experiment

27

Figure 11. Two-dimensional grid for Vauclin's infiltration experiment simulations

28

Figure 12. Initial pressure distribution

29

Figure 13. Experimental pressure and hydraulic-conductivity relationships

29

Figure 14. Moisture retention function, van Genuchten model-Vauclin's experiment

30

Figure 15. Moisture-retention function, Haverkamp modelVauclin's experiment

30

Figure 16. Moisture-retention function, Brooks and Corey model-Vauclin's experiment

31

Figure 17. Hydraulic conductivity-pressure relationship, Haverkamp model-Vauclin's experiment

31

Figure 18. Schematic plan view of WES Example Problem 1 . . . .

32

Figure 19. Areal view of WES Example Problem 1

33

Figure 20. Head distribution for WES Example Problem 1

52

Figure 21. Simulation of a continuous source, Case 1 at time 2,800 days

56

Figure 22. Concentration contours, Case 1 at time 2,800 days ...

56

Figure 23. Comparison of solution technique, Run 1 concentration contours

58


58

Figure 25. Simulation of a slug source, Case 2 at time 3.96 days

.

59

Figure 26. Simulation of a slug source, Case 2 at time 10.59 days .

59

Figure 27. Simulation of a slug source, Case 2 at time 16.59 days .

60

Figure 28. Continuous source in a radial flow field, Case 3

63

Figure 29. Concentration contours, Case 3, Test 1 at Day 20 ... .

63

VI


64

Figure 31. Concentration contours, Case 3, Test 2 at Day 20 ....

64


65


65


66

Figure 35. Column drainage simulation, Fresno medium sand ...

72

Figure 36. Effect of saturated hydraulic conductivity, Fresno medium sand

73

Figure 37. Effect of time step on Fresno medium sand column drainage

73

Figure 38. FEMWATER computer details

81

Figure 39. Comparison against analytic solution

84

Figure 40. Comparison against 3-D analytic solution

85

Figure 41. LEWASTE features

85

Figure 42. Water table elevation: Experimental and simulated results

89

Figure 43. Water table simulation

94

Figure 44. Simulated water table versus experimental data

95

Figure 45. Injection well in radial flow domain

95

Figure 46. Saturation profiles for water (+) and total liquid (o) saturations at the end of three stages

103

Figure 47. Effluent trends at Node 1; simulation becomes unstable after 220 days

104

Figure 48. Oil saturation profile at the end of Stage 1

105

Figure 49. Oil saturation profile after 25 days of redistribution (end of Stage 2)

105

Figure 50. Oil saturation profile after 45 days of redistribution . .

106

Figure 51. Oil saturation profile after 25 days of redistribution (end of Stage 2, Example 3)

106

Figure 52. PCE liquid phase saturations after release of 0.5 m3 over 7.5 hr

108

Figure 53. PCE liquid phase saturations after release of 2 days of redistribution in a homogeneous medium

108

Figure 54. PCE liquid phase saturations after release of 4 days of redistribution in a homogeneous medium

109

Figure 55. PCE liquid phase saturations after release of 2 days of redistribution in a mildly heterogeneous medium

..

109

Figure 56. PCE liquid phase saturations after release of 4 days of redistribution in a mildly heterogeneous medium

. .

110

Figure 57. MOC highlights

113

Figure 58. MODFLOW highlights

114

Figure 59. MODFLOW vendors

115

Figure 60. MT3D highlights

117

Figure 61. PLASM features

118

Figure 62. RANDOM WALK highlights

119

Figure 63. RAND3D highlights

120

Figure 64. FEMWATER characteristics

121

Figure 65. LEWASTE characteristics

122

Figure 66. UNSAT1 highlights

123

Figure 67. CHEMFLO characteristics

124

Figure 68. PRZM-2 overview

125

Figure 69. SUTRA highlights

126

Figure 70. VS2DT characteristics

128

Figure 71. MOFAT highlights

130

Figure 72. General groundwater software vendors

130

List of Tables Table 1.

Model Classification

Table 2.

Models Selected for Further Evaluation

4 17

VII

VIII

Table 3.

Values of Physico-Chemical Parameters for Case 1 . . .

22

Table 4.


23

Table 5.


24

Table 6.

Aquifer Properties for WES Example Problem 1 . . . .

33

Table 7.

PLASM and RANDOM-WALK Differences

53

Table 8.

Support Software for MODFLOW

115

Preface

The work reported herein was conducted by the Environmental Laboratory (EL), the Coastal and Hydraulics Laboratory (CHL), and the Information Technology Laboratory (ITL) of the U.S. Army Engineer Waterways Experiment Station (WES), Vicksburg, MS. The research was sponsored by the Department of Army Installation Restoration Research Program (IRRP), Environmental Quality and Technology, Work Unit entitled "Groundwater Model Assessment," Project No. AF25-GW-001. Dr. Clem Myer was the IRRP Coordinator at the Directorate of Research and Development, Headquarters, U.S. Army Corps of Engineers (HQUSACE). Dr. Bob York of the U.S. Army Environmental Center and Mr. Jim Baliff of the Environmental Restoration Division, Directorate of Military Programs, HQUSACE, served as the IRRP Overview Committee. Mr. Ira May and Ms. Tomiann McDaniel were Technical Monitors for the IRRP. Dr. Jeffery P. Holland, WES, was the Groundwater Modeling Program Manager. Dr. M. John Cullinane, WES, was the IRRP Program Manager. The study was conducted by Drs. Carlos E. Ruiz, Mansour Zakikhani, and Patrick N. Deliman and Mr. Christian J. McGrath of the Water Quality and Contaminant Modeling Branch (WQCMB), Environmental Processes and Effects Division (EPED), EL; Mr. Stacy Howington of the Reservoir Water Quality Branch and Mr. Robert A. Evans of the Estuarine Simulation Branch, Estuaries Division, CHL; and Dr. Fred T. Tracy of the Interdisciplinary Research Group (IRG), Computer-Aided Engineering Division (CAED), ITL. The study was conducted under the direct supervision of Dr. Mark S. Dortch, Chief, WQCMB, and under the general supervision of Dr. Richard E. Price, Chief, EPED, and Dr. John Harrison, Director, EL. This report was reviewed by Drs. Holland and Cullinane. At the time of publication of this report, Director of WES was Dr. Robert W. Whalin. Commander was COL Bruce K. Howard, EN.

IX

This report should be cited as follows: Ruiz, C. E, Zakikhani, M., McGrath, C. J., Deliman, P. N., Howington, S., Evans, R. A., and Tracy, F. T. (1997). "Documentation on limitations and applicabilities of the use of off-the-shelf groundwater models in site cleanup," Technical Report IRRP-97-4, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.

The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products.

Conversion Factors, Non-SI to SI Units of Measurement

Non-SI units of measurement used in this report can be converted to SI units as follows: Multiply

By

To Obtain

feet

0.3048

meters

miles (U.S. statute)

1.609347

kilometers

pounds (mass)

0.4535924

kilograms

I

XI

1

Overview

The U.S. Army Engineer Waterways Experiment Station (WES) Groundwater Modeling Team initiated a project in fiscal year 1992 (FY92) to determine the state of groundwater modeling as applied to Army remediation needs. The evaluation of groundwater models against observations from welldefined, multidimensional, field- or large-scale laboratory experiments will provide the user community with a tool to promote the acceptance of modeling efforts. Thorough evaluations will provide the older "mature" codes the confirmation and acceptance that until now has eluded them because they were applied with mixed success in groundwater problems. The objective of this report is to provide detailed and complete technical guidance to the Department of Defense (DoD) environmental restoration community in the selection of appropriate groundwater models and their application to subsurface remediation issues. This is an expressed need of DoD personnel responsible for environmental restoration of military installations.1 An assessment of the assets and limitations of selected codes for application to DoD groundwater remediation efforts is needed to assist decision makers in the selection of the best modeling approach in support of remedial design/operation. Code selection and application to remediation efforts likely will require defense in any judicial proceedings. The use of thoroughly and successfully evaluated models establishes the technical and institutional validity of model selection in such potential litigations. Results of this evaluation exercise will provide evidence that can be used by practitioners to advocate (or protest) the use of a particular model for a project. Use of an appropriate and well-documented model for remediation design will assist in negotiations with regulatory agencies, other responsible parties, or subcontractors. Guidance regarding the minimal (and preferred) documentation needed for the application of any groundwater modeling project is essential. This guidance includes suggestions regarding the minimal amount and types of

As expressed at the ARMY Groundwater Modeling Uses and Needs Workshop, 31 March -1 April, 1992, Denver, CO.

Chapter 1 Overview

information that should be recorded (if not included) in official documents detailing the application of numerical modeling to a remediation project. Such information should include, for example, descriptions of and rationale for the perceived conceptual model, numerical model selection and implementation, selection of calibration targets or tolerances, quantitative calibration assessment, and sensitivity analyses. Results from a rigorous, quantitative evaluation of a select suite of groundwater flow and transport codes can be used as a pattern for future model application. This suite of codes will be sufficiently diverse to meet present Army needs.

Chapter 1 Overview

Literature Review and Model Selection Initial Screening The initial screening was a broad review of available groundwater models and an assessment of Army modeling needs. The goal of the initial model inventory was to assemble a list of reasonably available codes. Obtaining information on many of the codes in the initial list was impeded by lack of widespread documentation (e.g., gray literature or proprietary codes). Appendix A contains the initial list of groundwater codes compiled as part of the literature review of this investigation. However, the list will require maintenance to include new and upgraded models and more information on existing models as such becomes available. The list was originally compiled as a "living document," which will be updated as part of future model evaluation reports. Groundwater modeling will continue to evolve for the foreseeable future, probably at an accelerating pace and so will the list of models. Monitoring this model development and providing guidance are important services DoD can provide to Army groundwater modeling efforts. Groundwater model selection depends upon the complexity of the remediation problem, the stage of site evaluation, time and financial constraints, and the capability of the model user. No single code or model package approaches the complete coverage of the flow and transport processes relevant in remediation modeling. Most remediation efforts do not, however, require modeling of all possible transport processes, which is fortunate since the data are rarely available for such a level of modeling. The objective of the literature review of groundwater models was to compile a guide that could provide the following: a. An extensive list of existing groundwater models grouped in selected categories, including a brief description and source/vendor/ distributor. b. Identification of Army groundwater remediation problems and modeling requirements. c. Identification of the transport processes requiring consideration in order to address required remediation modeling. Chapter 2 Literature Review and Model Selection

Classifications of Models Existing models were classified according to their key flow and transport processes or special applications (Table 1). This classification was adopted in order to help the user identify appropriate groundwater models for their application. Currently most of the groundwater modeling applicaTable 1 tions deal with saturated flow modelModel Classification ing (pump and treat) and in some occasions saturated flow and transSaturated (Flow and/or Transport) port simulations (Hadala et al. 1993). Unsaturated (Flow and/or Transport) Coupled Unsaturated/Saturated The above statement applies to both (Flow and/or Transport) the Army, DoD, and in general and Multiphase (Flow and/or Transport) the private sector (Hadala et al. 1993; Geochemical Models Geraghty and Miller 1992). Conditions (flow, media, and contaminants) are usually established early in the site assessment or remedial investigation process so that an informed model selection is possible. Knowledge of media properties such as hydraulic conductivity, porosity, and specific storage in addition to the flow domain allows the user to select a specific class of groundwater model to solve a distinct problem. As more site knowledge is acquired through the development of a conceptual model, the user can then select a code not only from a particular class of model but with special formulations to address the individual program. Site knowledge such as the existence of homogeneous, heterogeneous, layered, isotropic, or anisotropic domain (aquifer) allows the user to narrow the selection process to those models whose assumptions satisfy the conceptual model. For example, to simulate a fairly homogeneous saturated confined aquifer, the user must select a model from a decision tree. The first level of decision would be between analytic or numerical models for saturated flow; the next decision level could be the dimension of the modeling approach (one-, two-, or three-dimensional); the following decision may be between flow or flow and transport models; and conceivably another decision level could involve transport processes to be included in the flow and transport models. Knowledge acquired during the development of the conceptual model should drive the model selection process and vice versa. Appendix A meets the first objective of the literature review by providing an extensive list of available groundwater models. Appendix A follows the classification of Table 1 with the addition to subcategories like analytic solutions. Categories not covered in this report are flow and transport in fractured media, bioremediation, inverse modeling, stochastic modeling, and optimization. Models for bioremediation, inverse problems, optimization, stochastic modeling, and other special categories were beyond the scope of the current review. Reviews of models in these categories will be undertaken as part of other Groundwater Modeling Team efforts.

Chapter 2 Literature Review and Model Selection

Hadala et al. (1993) document a first cut at identifying Army needs, problems, and modeling needs in remediating contaminated groundwater sites. The current effort provides the user a companion to a model's user guide. The document describes several model applications that can help the user in applying the evaluated codes to specific sites. In addition, the report reviews and evaluates several groundwater models that cleanup specialists might apply in the near future, thus providing a reference source. Appendix B of this report is a summary of processes requiring consideration if remediation modeling of organic contaminants is going to be successful. Most of the transport models evaluated herein contain a subset of the processes described in Appendix B. The processes incorporated in each specific model will be described and discussed in the model evaluation section. In addition to the processes described in Appendix B, contaminant degradation is an important process. Most contaminant transport models include either a first order, a zero order, or a combination of first and zero order degradation rates. First and zero order degradation rates are relatively easy to incorporate in either numerical or analytic groundwater models.

Groundwater Modeling The use of groundwater models, in particular numerical groundwater models, has escalated in recent years due in part to regulatory pressures, innovative technologies, and the high cost of intensive sampling. This section is a primer or review of saturated and unsaturated groundwater flow and transport. The emphasis is to present the mathematical formulations on which most current groundwater models are based. It is intended as a primer and a reference source. Saturated Groundwater flow in saturated media is based on Darcy's law. Darcy found that the one-dimensional flow of water through a pipe filled with sand is proportional to the cross-sectional area of the pipe and the head loss along the pipe and inversely proportional to the flow length (Fetter 1993). The mathematical formulation can be expressed as al where Q = volumetric discharge K = proportionality constant known as hydraulic conductivity A = cross-sectional area dhldl = gradient of hydraulic head


Darcy's law can be expressed in terms of the specific discharge or Darcy's flux, q, which is the volume of water flowing per unit time through a unit cross-sectional area. Darcy's flux, q, is also defined as QIA. vdh q = -K— dl

(2)

The specific discharge or Darcy's flux, q, represents the flow per unit cross-sectional area of the column or medium that also includes the solid matrix. The average velocity (seepage velocity) only considers the portion of the area available to flow, that is eA; thus, the average velocity, V, of the flow through a column is

V=4=Ä eA

(3)

e

Darcy's law is applicable for most groundwater flow conditions but begins to deviate from observations at high-flow velocities (small Reynolds number) that may be encountered near large pumping and recharging wells, flow through cavernous material such as limestone, and flow through breakwaters constructed of gravel or large stones. Flow through very fine grained media (usually not in aquifers) is also not described well by Darcy's equation (Bear and Verruijt 1987). The hydraulic conductivity or coefficient of proportionality, K, can be defined as the specific discharge per unit hydraulic gradient and has units of velocity {LIT). Hydraulic conductivity depends on both fluid properties and soil matrix properties. Fluid properties that influence the hydraulic conductivity are the density and viscosity of the fluid. The relevant solid matrix property is related to grain-size distribution, grain shape, surface area, and porosity. Thus the hydraulic conductivity can be expressed in terms of the permeability, which only depends on the soil properties K = ** = ** \i

V

(4)

where g = acceleration of gravity p = liquid density |i = liquid viscosity v = kinematic viscosity k = permeability of porous medium Bear and Verruijt (1987) and Maidment (1993) provide typical values for hydraulic conductivity and permeability for different aquifer materials. A porous medium is said to be homogeneous with respect to permeability if the permeability is the same at all points. Otherwise, the porous medium is said to be heterogeneous; permeability varies from point to point. If the permeability is independent of direction, then the porous medium is Chapter 2 Literature Review and Model Selection

said to be isotropic. If the permeability varies with direction, then the medium is said to be anisotropic. Both permeability and hydraulic conductivity (as well as other porous media properties) can exhibit anisotropy. Aquifers are often anisotropic. Hydraulic gradient is a vector, having both magnitude (a value) and direction. Hydraulic conductivity is a tensor, thus described by nine components. If the coordinate system is oriented along the principal axes, the tensor becomes

0 Kyy 0 0 Kzz T 0

K

xx

0 0

K =

(5)

and for the isotropic case becomes K = Kxx = Kyy = Kzz. For isotropic porous medium, Darcy's law in three dimensions becomes q

= _K)

(14)

where q = soil moisture flux K(*¥) = unsaturated hydraulic conductivity at a given *F ^W) = gradient of total soil-water potential,


11

Water-Retention Functions 1. Haverkamp et al. (1977)

0 (h) = 6

+

g [6s

Q

^s]

[a+(ln|A|)*]

6 (h) = 6C

for h < -1 for h > -1

2. van Genuchten (1980)

[6s e eS ] 6(A) = eres ", T K res+ — [l+(a\h\)b ]m

for h0

where m = 1 - 1/b 3. Brooks and Corey (1964) 6(A) =Qzes+ies-eres]{^}b

for h 0

4. Campbell (1974)

6(A) = 0Ss (^)

b

h

6 (h) = 6S 0S 0res 0(h) pe b Figure 2.

12

for h p,e

= saturated water content or porosity = residual water content = volumetric water content at matric potential h = entry or bubbling capillary pressure = empirical parameter Soil-water retention relationships


Hydraulic Conductivity Functions 1. Haverkamp et al. (1977) KT(M " »"/

= **■& K

a

—.

fnr h ">» " u fl IUI II

,

{*+\h\b}

K{h) = Ks

for h>0

2. van Genuchten (1980) F(h) - F '^-(alAl)*-1

[l+(a|22|)*]-»}2

for h < 0

{l+(a|J2|)b}2 K{h)

for h>0

= Kg

where m = 1 - 1/b

3. Exponential K(h) = Ks exp (Jbh)

for h < 0

K(h) = Ks

for h>0

4. Campbell (1974)

iC(h) = Xs (^)

*

K(h) = Ks

K(h) Ks pe b Figure 3.

= = = =

for

h
pe

soil hydraulic conductivity at matric potential h saturated hydraulic conductivity entry or bubbling capillary pressure empirical parameter Hydraulic conductivity relationships


13

The governing differential equation for fluid flow through porous media is obtained from continuity and Darcy's law. A general form of the mass balance can be expressed as:

{Mp(.-)«+epß] + ep^p!dt

ev

(15) +

e5

dp_dC dC dt

H-^— " V«JTVCT -ß = 0

where ev = total pressure head, pc + pgz K = hydraulic conductivity tensor Q = flow point sources/sinks a = pore volume compressibility ß = liquid compressibility C = solute concentration The term dSJd§ev is the specific moisture capacity and relates to the soil's pressure saturation relationship in the unsaturated zone. Unsaturated codes solve Equation 15 with appropriate boundary and initial conditions for the pressure (matric head) distribution. The velocity field is then estimated from the pressure head and Darcy's law (Darcy-Buckingham). The velocity field is used to solve for the associated contaminant transport. A general form of the contaminant mass balance in unsaturated porous media can be written as: jt(epSwC) + jt{pbS) + V.{epSwqC) (16) = V.(epSwD).VC + ep5w*P + pb¥s QpC* where C = solute concentration in liquid phase S = solute concentration on solid phase Pk = soil bulk density D = tensor, which includes both diffusion and dispersion *F = rate of solute degradation/production in liquid phase v

¥s = rate of solute degradation/production in solid phase

Qp = rate of liquid injection/withdrawal C* = solute concentration in fluid source/sink Equilibrium sorption models can be used to define the solid phase concentration in terms of the liquid phase concentration, C. Three equilibrium 14


Sorption isotherms are described in Appendix B, Part 1; in all three models, the solid phase solute concentration, S, is a function of C(S =/(Q). The general equation for sorption is:

f = f(C)f at at

(17)

where /(C) is the solute concentration in the solid phase and is a function of fluid concentration, C. The production/degradation terms for both liquid and solid phases account for chemical, biological, and/or physical reactions in the soil water or soil surface. The production/degradation rate for the solute in liquid phase is usually assumed as either first order or zero order:

¥ = xxc or

(18)

where X-j is the first-order rate constant, and XQ is the zero-order rate constant for the liquid phase. The solute rate in the solid phase rate is analogous: % =JlS

(19)

where y^ is the first-order rate constant for the solid phase. Equation 19 can be written in terms of the solute in the liquid phase assuming linear sorption: % =

yiKdC

(20)

where K^ is the linear partition coefficient, discussed in Appendix B, and all other terms have been previously defined. Degradation refers to reactions that decrease the solute; production refers to increase due to formation of the solute.

Model Selection The initial list of models considered for evaluation is included in Appendix A. The list was reduced to a manageable suite, and the shorter list of models were further evaluated and summarized in this document. Criteria for this model screening were defined based primarily on current and anticipated Army needs (Hadala et al. 1993). The criteria used to select the models for the short list were the following: a. Model and code are well documented. b. Model has been previously tested.


c. Code/model meets the Army groundwater cleanup needs. d. Source code is available. e. Code is in the public domain. The first criterion allowed selection of codes that are mature. Mature codes have fewer errors, have larger database of users, and have been applied to a variety of problems. The documentation of mature codes is usually satisfactory; if the code has undergone significant revisions, the documentation tends to be good. Some of the codes that were selected are not mature codes, but other factors influenced their selection. The selection of the codes for further evaluation was influenced by previous model evaluations (Celia, Gray, and Hassanizadeh 1992; van der Heijde and Elnawawy 1992; Beljin 1988; Kincaid and Morrey 1984; Morrey, Kincaid, and Hosteller 1986; Wagner and Ruiz-Calzada 1987) and groundwater model reviews (Moskowitz et al. 1992; OS WER 1989, 1990; Mangold and Tsang 1991; Faust and Mercer 1980; Mercer and Cohen 1990; and Geraghty and Miller 1992). Beljin (1988) evaluated three codes, SEFTRAN, MOC, and RANDOM WALK, two of which were selected for further evaluation in this effort. The selection of codes that were previously evaluated and are very popular allows the authors to confirm the previous evaluation/validation and provides additional knowledge to future users. Hadala et al. (1993) and Geraghty and Miller (1992) found that MODFLOW was the most used code in both Army and the U.S. Environmental Protection Agency (EPA) groundwater communities, respectively. Other popular codes from the surveys were RANDOM WALK and USGS-MOC. PRZM II was selected because it is the only unsaturated zone model that includes contaminant interaction in the root zone. Three coupled unsaturated-saturated zone models, FEMWATER/LEWASTE, VS2DT, and SUTRA, were selected because of their ability to solve both unsaturated and saturated zone problems. An additional reason for selecting FEMWATER/ LEWASTE was its selection as the code of choice for wellhead protection analysis by EPA. MOFAT was selected because it is one of the few compositional multiphase flow models for which source code is available in the public domain. The codes selected for further evaluation were grouped according to the classification of Table 1. The list of models evaluated is presented in Table 2. The codes were recommended for evaluation because of their popularity, maturity, properties, and/or flow and transport processes and pathways. CSU-GWFLOW and TRANSPORT evaluation will be documented in a contractor report.

16


Table 2 Models Selected for Further Evaluation Saturated (Flow and/or Transport)

Unsaturated (Flow and/or Transport)

Coupled Unsaturated/ Saturated (Flow and/or Transport)

Multiphase

MOC

UNSAT1

FEM WATER

MOFAT (MOTRANS)

MODFLOW

CHEMFLOW

LEWASTE

MT3D

PRZM II

SUTRA

PLASM

VS2DT

RANDOM WALK/RAND3D CSU-GWFLOW CSU-TRANSPORT

Model Evaluation, Verification, and Validation The purpose of the model evaluation is to provide an independent assessment on the applicabilities and limitations of the selected codes in solving ground water contamination problems. The evaluation described in this report is a first step in a series of stages that constitute a validation protocol. In the first step, computer code, mathematical formulations, and numerical formulations were tested and evaluated. The testing included examples included with the code, problems described in the literature, and experimental data. All models were not subjected to the three levels of testing due to lack of either experimental data or available analytical solutions. Lack of available analytic solutions applies to both unsaturated flow and transport and multiphase flow. The evaluation effort includes scrutiny of the code structure and performance evaluation relative to appropriate problems for which analytical solutions are available. The models were evaluated independently, and their performance in matching both flow and transport, as applicable, is documented. The summary on each evaluation includes the following: a. Model description. b. Platform for evaluation (personal computer (PC), workstation, mainframe). c. Model performance in solving example problems included with the code. d. Modifications, if any, for the evaluation. e. Model performance in solving the "typical" scenarios: inputs, results, and comparisons. /.

Recommendations.


17

Similar evaluations/verifications have been proposed by State and Federal agencies. The State of Illinois has eight standards that must be met to accept a computer code for landfill permitting. The standards include the following: check model documentation; check mathematical equations; check numerical solution; model calibration against site-specific data; sensitivity analysis; mass balance checks; site-specific parameters shall be based on laboratory or field data; and nonsite-specific parameters need to be documented. Federal agencies like the EPA have hinted that future issuance of permits will be based on model application and testing, thus, the need of establishing testing and verification protocols. Model verification is the assurance that the computer code correctly performs the operations specified in the numerical model (Beljin 1988). The key in model verification is to check the accuracy of the computational algorithm used in the numerical code to solve the mathematical formulations. A second objective is to make sure that the computer code is fully operational; that is, all options are operational. Model validation provides the assurance that the algorithms embodied in the computer code correctly represent the physical processes or system to which the model is applied (Beljin 1988). Validation is an assessment of how the governing equations describe actual system behavior. A model is said to be validated when sufficient testing shows an acceptable degree of matching the actual systems. Although several authors have shown some disagreement on the use of the terms validation and verification of groundwater models (Konikow and Bredehoeft 1978; Anderseon and Woessner 1992), the key is that the users and regulators need some level of confidence associated with a given model. The level of confidence can be called validation, verification, or just plain confidence level, but model confidence is a fundamental issue if meaningful modeling studies are to be performed. To achieve model confidence, a multistep or multitiered model testing protocol is proposed. A multitiered assessment protocol consists of progressively evaluating the subject codes at rigorous levels of analysis. These levels are as follows: a. Evaluation of code structure and process formulations. b. Code performance on a set of problems for which analytical solutions are available. c. Code performance on synthetic benchmarks (hypothetical scenarios). d. Performance relative to laboratory experimental data (bench or artificial aquifer scale) e. Code performance relative to well-controlled, field-scale experimental data. Appropriate problems with analytical solutions are available for most model categories (Huyakorn and Pinder 1983). Highly reliable experimental data at the bench and field scale are limited or unavailable for several

18


categories of codes. All codes will be evaluated to assess their "ease-ofuse" or lack thereof, memory requirements, hardware requirements, and other features.


19

3

Test Cases

Overview The evaluation of groundwater codes requires the adherence to an established protocol as that proposed in the introduction of this report. In order to follow the proposed evaluation protocol, several test cases were selected. Each test case was selected to address a specific area of groundwater flow and transport modeling. Three issues that influenced the choice of the test cases were as follows: cases have been previously used by other authors on previous model testing; the test cases are well known in the groundwater literature; and availability of an analytic solution—if no analytic solution is available, then a laboratory experiment was selected as a test case. Test cases were selected for saturated flow and transport, unsaturated flow, and coupled unsaturated and saturated flow. The models were evaluated to different levels of code evaluation as described in Chapter 2. Saturated groundwater flow and transport models were evaluated to level two of the proposed testing protocol: code performance on a set of problems for which analytical solutions are available. Unsaturated and coupled unsaturated/saturated flow models were evaluated at levels one and four: code performance relative to laboratory experimental data. One saturated flow model, PLASM, was evaluated at levels one and three: code performance on synthetic benchmarks or hypothetical scenarios. As a final note, all codes were evaluated to assess their "ease-of-use" in setting up or solving the test cases. Any model modification to solve the selected test cases will be documented in the model evaluation and/or discussion.

Saturated The test cases selected for saturated groundwater flow and transport were three problems for which analytical solutions exist. The first criterion was in selecting the test problems previously used by other investigators: Beljin (1988) used them in evaluating four groundwater models, thus a 20

Chapter 3 Test Cases

larger database of models can be compared using these three problems. The second selection criterion was that other researchers have also used the test cases in evaluating their codes (Pinder 1973; Wilson and Miller 1978; and Wagner, Watts, and Kent 1984). The third criterion is that the test cases meet the objective of checking the accuracy of computer models since an analytic solution exists for the three problems. The three test cases are as follows: a.

A continuous source in a constant flow field (Case 1).

b.

A slug source in a constant flow field (Case 2).

c.

A continuous source in a constant radial flow field (Case 3).

The three test cases correspond to example problems used in Beljin (1988). The cross reference to Beljin's report is as follows: BM-I.3 (Case 1 in this report). BM-I.4 (Case 2 in this report). BM-I.5 (Case 3 in this report). Case 1. Two-dimensional solute transport from a continuous point source in a uniform groundwater field. The test problem has been documented by other researchers (Pinder 1973; Wilson and Miller 1978; Wagner, Watts, and Kent 1984; Beljin 1988) and consists of the continuous injection of a contaminant from a point source or a well into an aquifer. As a result of the continuous injection, a plume develops downstream from the injection point and spreads out laterally. For a thin aquifer, vertical mixing should occur, and the concentration becomes uniform with depth in the aquifer. When uniform vertical occurs, the plume can be regarded as essentially two-dimensional. The case history for the stated problem is based on the groundwater contamination with hexavalent chromium in South Farmingdale, Nassau County, New York (Wagner, Watts, and Kent 1984). The aquifer has a saturated thickness of 33.5 m with a porosity of 0.35. The average seepage velocity is 0.460 m/day and the estimated dispersivity values of aL = 21.3 m and ocT = 4.27 m. The source of contamination consisted of three metal plating waste-disposal ponds by the Liberty Aircraft plant in South Farmingdale. The estimated mass rate of contaminants entering the aquifer has been estimated at 23.59 kg/day (Beljin 1988). Adsorption and degradation can be neglected since chromium is relatively conservative. A summary of the parameters is presented in Table 3. Beljin (1988) used two grids in his evaluation, a coarse grid (Ax = 180 m, Ay = 60 m) and a fine grid (Ax = 60 m, Ay = 30 m). The Peclet number was 4.56 for the coarse grid and 2.91 for the fine one. For a time step of 100 days, the Courant numbers were 0.25 and 0.76 for the coarse and fine grid, respectively (Beljin 1988). Figure 4 shows a typical grid for Case 1 problem. Case 2. Transport of a solute slug in a uniform groundwater flow field. The problem analyzes the two-dimensional solute transport due to a slug injection of a conservative contaminant into a uniform flow field. This Chapter 3 Test Cases

21

Table 3 Values of Physico-Chemical Parameters for Case 1 Aquifer saturated thickness, b

33.5 m

110ft

Darcy Velocity, u

0.161 m/day

0.525 ft/day

Seepage velocity, u

0.460 m/day

1.5 ft/day

Porosity, n

0.35

Longitudinal dispersivity, aL

21.3 m

69.9 ft

Transverse dispersivity, xx = «L?f + O-THTJ + CCTVrr

M

M

+ D

M

(25>

*

where aL = longitudinal dispersivity [L] v = magnitude of the velocity vector [LT1] a

TH

=

horizontal transverse dispersivity [L]

a

TV

=

vertical transverse dispersivity [L]

D* = molecular diffusion [L2Tl] The general form of the reaction term in the transport equation is

t* - T17 - {x>c + ^c')

*=l

adsorption

(26)

decay

where C" = adsorbed concentration [ML'3] pb = bulk density of the medium [ML'3] Xi = decay or biodegradation rate for solute [F1] X2 = rate for adsorbate [7"1] The amount of contaminant adsorbed to the medium is assumed to be a function of the dissolved concentration only. Based on the type of isotherm chosen (linear, Freundlich, or Langmuir) the model computes a retardation factor due to adsorption. Reactions are applied based on gridaveraged concentrations. Within the above equations, the model has assumed the following: • Darcy's Law is applicable. • Porosities, dispersivities, and reaction parameters are constant in time. Numerical methods. MT3D uses a mixed Eulerian-Lagrangian solution scheme. Four options are provided for the simulation of the advection component of transport. These options are three Lagrangian-based, particletracking methods (MOC, MMOC, and HMOC) and a fixed-grid-based (Eulerian), block-centered, upwind finite-difference scheme. The MOC (method-of-characteristics) technique projects the future location of particles advected by the seepage velocities and produces very little numerical dispersion. The MMOC (modified-method-of-characteristics) tracks a single, cell-centered particle backward in time using the seepage velocities 48

Chapter 4 Models Description

to determine its location at the beginning of the time step. MMOC is more efficient than MOC but contains some numerical dispersion from the interpolation process. The hybrid-method-of-characteristics (HMOC) technique takes advantage of the strengths of each of these methods by using MOC near large concentration gradients and MMOC elsewhere in the field. Although very dispersive and not routinely recommended, upwind finite differences are included as an option for the advection term because, unlike particle schemes, they are mass conserving and computationally efficient. Dispersion, sources and sinks, and reaction processes are simulated by an Eulerian, block-centered, explicit finite-difference method. Evaluation. Performance of the MT3D model is evaluated by comparison to two sets of problems: (a) ten example problems provided with the model (Zheng 1992), and (b) three scenarios for which analytical solutions are available. Examples. MT3D is packaged with 10 example problems that range from model comparison against analytical solutions to sample applications in multidimensional heterogeneous media. The example problems demonstrate various features and capabilities of the model. The model was able to execute all 10 benchmarks provided with the code. The results compare well with analytical solutions where available and appear reasonable for problems with no analytical solutions. Problems with analytical solutions. Three synthetic benchmarks are defined for which analytical solutions are available. Analytical solutions included in the SOLUTE package (Beljin 1991) are adopted as the reference solutions for the following: a. A concentration plume emanating from a continuous point source in a uniform two-dimensional flow field. b. A concentration plume produced by a slug point source in a uniform, two-dimensional flow field. c. A concentration plume produced by radial transport from a fully penetrating recharge well in an infinite, planar aquifer. Continuous source in a uniform flow. Contamination was introduced at a constant rate through a fully penetrating well in a steady-state flow. The medium is an infinite, homogeneous, confined aquifer of constant thickness, and the recharge rate is negligible relative to regional flow. The PLUME2D - Point Source analytical solution is used. Comparisons are made with and without retardation and decay. The model performed very well in predicting both the magnitude and arrival time of the contaminant when modeled as a conservative tracer. Mass balance errors were acceptably small, ranging from 1 to 5 percent. Likewise, the MT3D concentrations predicted with retardation and decay matched closely with the analytical solutions. Again the mass balance errors were acceptable. Slug source in a uniform flow. Contamination was introduced in the initial condition to the model and allowed to disperse in a uniform, steady-state flow field. No decay or adsorption was simulated. MT3D matched the speed of the peak and approximated the amplitude very well.


49

The model tended to slightly overpredict the amplitude of the peak at early times. Some wiggles in the predicted peak can be seen, but are not considered significant. Overall, the mass balance error was an acceptable 2.5 percent at 16 days. Continuous source in a steady, radial flow. MT3D is not capable of discretizing a domain in radial coordinates. Therefore, a radial transport problem presents a significant challenge. A fully penetrating injection well was placed in an otherwise stagnant, confined, infinite, homogeneous medium. The well injects at a constant rate and establishes a steady-state flow field. The contaminant was introduced into the well at a constant rate of 1.0 ppm. The analytical solution was provided by the RADIAL program within the SOLUTE package. The MODFLOW/mt flow solution was generated in a finite domain by computing, by hand, the boundary values of head that would produce the desired flow and installing these as constant heads in the model. This flow field was then used for the MT3D simulations. The results show a generally circular spreading of the contaminant. There is no visible difference between the contaminant advancement along a gridline and diagonal to the gridlines. Comparison with analytical results show a good agreement for all three values of longitudinal dispersivity tested. The mass balance errors for these simulations ranged from about 6.5 percent at 20 days to less than 3 percent at 40 days. Summary. MT3D is a proprietary code that is the property of Dr. Chunmiao Zheng and S. S. Papadopulos and Associates, Inc. It is available for $450. The EPA's Robert S. Kerr Environmental Research Laboratory distributes MT3D Version 1.2 through CSMoS, but the model is relatively new and has not received the same degree of public scrutiny as many of the USGS models. The model's roots date back only about 6 years (Zheng 1988). The model has been in a form similar to today's version for only about 4 years. However, its current popularity and ties to the immensely popular MODFLOW program suggest that the model probably will be maintained and upgraded. The developer of the program has moved recently from SSP&A to the University of Alabama. SSP&A insist that they will continue to support and distribute the model and that they will continue to work with Dr. Zheng. Although upgrades are promised, his departure makes future upgrades to the program and to the MODFLOW/mt flow solver slightly less definite. Support for the model goes through SSP&A or Dr. Zheng. As of 1993, with the purchase of MT3D, users are entitled to 20 min of telephone support in the first year, the right to purchase, by contract, additional telephone support at about $2 per minute and notification of the availability of upgrades via a newsletter for registered users. MT3D assets for remediation simulation are many. The model simulates many important transport processes including advection, dispersion, different decay rates for the solute and the adsorbed contaminant, and sorption. This makes MT3D vastly superior to pathline codes that only track the advective component of transport. The particle-based Lagrangian approach is superior to coarse-grid Eulerian schemes for simulating advection-dominated problems. Steep 50


concentration gradients can be simulated without smearing of peaks. The model can accept steady-state or transient-flow solutions. This is a very important attribute for remediation. It is unlikely that the hydrologic stresses will remain constant over the life of a remediation project. The developer considered computational speed and memory requirements when building the model. Several examples are readily available. Regions of the flow domain that will not experience contamination can be declared inactive for transport computations. Also, particles for the MOC solution are allocated dynamically. In this manner, particles are only introduced where contamination exists. The use of MMOC away from concentration gradients is driven by computational speed and memory considerations. This attention to detail makes the MT3D model well suited to microcomputer application—even for large problems. MT3D limitations in remediation modeling stems mostly from inherent problems with MOC-type methods in conserving mass. Mass conservation is difficult to ensure with particle-based codes. Mass balance errors less than 10 percent are considered acceptable. There are very many options in the numerical implementation of the advection process. The user is asked (permitted) to select planes of particle introduction, maximum and minimum numbers of particles, critical concentration gradients, etc., that have no meaning for someone unfamiliar with the inner workings of a particle-tracking program. Manipulation of these model parameters is sometimes necessary to achieve a stable, physically meaningful answer with an acceptable mass balance error. Unlike some of the more complicated transport codes, this model is limited to small concentrations. The transport code is completely decoupled from the flow solution. This precludes the simulation of flows that are affected by contaminant concentrations (density-dependent problems). Overall, for a saturated medium in which the flow and transport solutions can be decoupled (density variations are small), the use of MODFLOW/mt with MT3D is highly recommended. The models are sufficiently simple that set up, and modification can be performed in a reasonable time frame. However, when combined, these models have most capabilities required for routine flow and transport modeling. MT3D will be included in the GMS in late FY95. PLASM The Prickett-Lonnquist Aquifer Simulation Model (PLASM) is a groundwater flow simulation model. The model was developed for the Illinois State Water Survey (Prickett and Lonnquist 1971) and has been modified extensively. Some of the modifications and/or extensions are RANDOM WALK (Prickett, Naymik, and Lonnquist 1981a,b), GWFL3D (Walton 1989), CONPLASM, and UNCPLASM. The model and extensions reviewed in this report are those distributed by the IGWMC (IGWMC-FOS12). The model is distributed as a package of three finite difference codes: PLASM, CONPLASM, and UNCPLASM Chapter 4 Models Description

51

and PREPLASM, a preprocessor. PLASM simulates two-dimensional transient flow of groundwater in heterogeneous, anisotropic, fully confined aquifers. CONPLASM is a modification of PLASM that solves twodimensional transient flow in fully confined and leaky confined aquifers. UNCPLASM is a version of PLASM that solves the two-dimensional transient flow in unconfined or water table aquifers. Overview. PLASM is a two-dimensional finite difference model that uses an iterative alternating direction implicit scheme in solving the governing unsteady-state groundwater flow in a confined, nonhomogeneous, and isotropic aquifer. The code is a block-centered model. PLASM requires the user to assign either storage coefficient or specific yield to the cell (area around the nodes) and to specify transmisivities to the cell faces (area between the nodes) (Anderson and Woessner 1992). Evaluation. The code was evaluated with the four example data sets included with the documentation. One problem tests the no-flow boundary option, one the constant head option, a third tests the ability of running multiple wells, and the fourth is a regional groundwater system with multiple boundary condition options. The code was able to solve all four problems included in the documentation. Hypothetical scenario. The model was tested with the WES Example 1 discussed in Chapter 3. Figure 20 shows the head distribution for the WES Example Problem 1. Overall, PLASM results compared favorable with results from other models like CSU-GWFLOW and RANDOM-WALK. Table 7 presents the difference between RANDOM-WALK and PLASM for confined and unconfined cases. NO FLOW BOUNDARY

e.ee

62S.ee

SCALE 1

Figure 20.

52

J_l Mill i2se.ee i87s.ee

inch = 555.6 dole un u»

2see.ee

312S.1

NO FLOU BOUNDARY

Head distribution for WES Example Problem 1


Table 7 PLASM and RANDOM-WALK Differences Unconfined

Confined

Recharge, Percent Difference

Pumping, Percent Difference

Recharge, Percent Difference

Pumping, Percent Difference

0.000

0.000

0.000

0.000

0.036

0.044

0.111

0.515

0.035

0.087

0.249

0.960

0.145

0.130

0.527

1.258

0.124

0.137

0.082

1.242

0.378

0.140

0.030

1.247

0.440

0.127

0.225

1.250

0.485

0.105

0.365

1.228

0.518

0.085

0.479

1.180

0.528

0.062

0.557

1.111

0.520

0.037

0.600

1.009

0.496

0.020

0.595

0.876

0.439

0.000

0.547

0.718

0.344

0.008

0.437

0.521

0.201

0.006

0.271

0.291

0.000

0.000

0.000

0.000

Summary. PLASM is a two-dimensional groundwater flow model. It is a mature code with significant support from third-party vendors. One third-party software used in the evaluation was PREPLASM, distributed by the IGWMC. PLASM is an excellent teaching tool and very useful in testing conceptual models. In an ideal world, a preliminary simulation would be performed with PLASM to adjust the major parameters, and then, after obtaining good agreement with site-specific data, a more comprehensive model would be run. RANDOM WALK The RANDOM-WALK algorithm for solving solute transport in groundwater was developed by Thomas Prickett of the Illinois State Water Survey (Prickett, Naymik, and Lonnquist 1981a,b). The original RANDOM WALK model consisted of PLASM coupled with a "random walk" solute transport model. The model simulates one- or two-dimensional contaminant transport. The transport of contaminants is simulated by moving "particles" with both advection and dispersion. It uses groundwater velocities to compute the advection part of the displacement and a MONTE CARLO method for Chapter 4 Models Description

53

determination of displacement due to dispersion. In addition, the model simulates the effects of chemical reactions. The RANDOM-WALK algorithm has been coded into both two-dimensional (RAND2D)1 and three-dimensional (RAND3D) models. Comparisons of the two-dimensional (RANDOM WALK) model with analytic solutions for three cases was performed by Beljin (1988). Beljin (1988) used the IGWMC version of RANDOM WALK (original model). RAND3D and RAND2D are modifications of the original RANDOM WALK by Thomas Prickett and other contractors. Objective. The first objective of this study was to test both the IGWMC version of RANDOM WALK and the three-dimensional solute transport model RAND3D using three test cases: a. A continuous source in a constant flow field (Case 1). b. A slug source in a constant flow field (Case 2). c. A continuous source in a constant flow field (Case 3). These cases correspond to three cases used in Beljin (Beljin problems BM-I.3 (fine grid), BM-I.4, and BM-I.5 correspond to Case 1, Case 2, and, Case 3, respectively). In order to compare RAND3D with the twodimensional results, the three-dimensional model aquifer was set up to be, in essence, a two-dimensional problem. This meant that there was no variation in geohydrologic parameters in the x-y plane. The second objective was to determine the degree of difficulty in using RAND3D and its applicability to complex groundwater geometries. To avoid duplication of efforts, the IGWMC version of RANDOM WALK was only tested against the sample data sets included with the distribution diskette. Overview. RANDOM WALK was evaluated to level one following the protocol described in Chapter 2. The manuals included in the IGWMC version were Bulletins 55 and 65 from the Illinois State Water Survey (Prickett and Lonnquist 1971; Prickett, Naymik, and Lonnquist 1981a,b). The documentation was good. The model is an adaptation of the mainframe code RANDOM WALK developed by Prickett, Naymik, and Lonnquist 1981a,b. The code is written in FORTRAN and was compiled with Microsoft FORTRAN Version 3.2. The model was tested against the three examples included in the distribution diskette. The results were satisfactory when compared against the results in the original manual. RAND3D was selected for further evaluation (level two) because the model is an extension into three dimension of the original one- or two-dimensional RANDOM WALK.

Prickett refers to the two-dimensional model as TRANS. For consistency with RAND3D, TRANS will be referred to as RAND2D.

54


There are significant limitations to the use of RAND3D as it exists at present. These limitations concern the type of platform the code must run on and the maximum size of the problem allowed. RAND3D is written in BASIC and must be run on IBM-PC or compatible machines under the MS-DOS operating system. The machine must have 640 K of memory. It is an interactive program that uses the Microsoft Quick BASIC graphic routines. This limits the use of the program to fairly small, simple problems. Larger, more complicated problems would require more layers, more grid points, and more particles. The present limits are 3 layers, 40 rows, 40 columns, and 10,000 particles. In addition, larger problems in the foreseeable future will require significant amounts of computer time. It would be preferable to run these on mainframes or work-stations. In order for this to be done, the code must be rewritten so that it is completely portable. This would require conversion to a standard language (FORTRAN or C) and the removal of machine-dependent graphics. Input/output parameters. RAND3D requires that at least two layers be defined. In order to make comparisons with the two-dimensional cases, transport should only be in a single, homogeneous aquifer. This was simulated by defining the lowest layer (layer 1) in RAND3D such that no transport occurred there. This was accomplished by setting the sources exclusively in the second layer, defining the vertical dispersion in all layers to be 0, and setting the flow velocities in the lowest layer to 0. Also, the vertical velocities in all layers were set to 0. Case 1, Continuous Source in a Constant Flow Field: This case used an aquifer with the following geohydrologic and model parameters: aquifer thickness, b Darcy Velocity, v Porosity, n Mass/Particle, M Particles Time Total Mass Injected Dmax Zmax Longitudinal Dispersivity, aL Transverse Dispersivity, ar No Retardation No Decay Number of Rows (Y dimension) Row Spacing Number of Columns (X dimension) Column Spacing

110ft (undefined in 2-D case) 0.525 ft/day 0.35 29.12 lb/particle 5,000 2,800 days 52 lb 10ft 1ft 70 ft 14ft 19 98.4 ft 36 196.8 ft

The source of contamination is a continuous source along a line that is centered at X = 500 ft, Y = 900 ft and is throughout the second aquifer layer (110 ft). Figure 21 shows the RAND3D, RAND2D, and the analytic solutions of Case 1 for a cross section through Y = 900 ft. This shows good agreement with both the two-dimensional and analytic solutions. Figure 22 shows Chapter 4 Models Description

55

Continuous Source in a Constant Velocity Field Simulation Time 2800 Davs

80 70 60 50' 40' 30'

o U

20' 10-

t • •

-1000

1000

2000

3000

4000

5000

6000

7000

Range from Source, feet

Figure 21.

Simulation of a continuous source, Case 1 at time 2,800 days

0.525 Uihy >■

Model Paremelerc: 5000 Panicles 29.12 lbs/panicle DmiXM 10 Zrnix« 1 Decoy*0 No Retardation

Geologic Puanicten: Porosity, D ■ 035 aL» 70 feet aT> 14 feet tXj" Ofcel

(10O.1OO)

Figure 22.

56

Concentration contours, Case 1 at time 2,800 days


the RAND3D-predicted plume formed by the source at a simulation time of 2,800 days. Note that it is not symmetric. This is due to the random nature of the solution technique. This random nature of the model also explains why there is mass upstream from the source. One of the characteristics of the RANDOM-WALK method is that one will get a slightly different answer every time it is run. Figures 23 and 24 illustrate this point. These simulations were done using the same identical inputs (note that the parameters are not identical with the parameters above), but were done at different times. There are variations. There are two possible solutions to this problem. The first is to increase the number of particles used. The second is to do multiple runs and compute the average (and perhaps standard deviation). Case 2, Slug Source in a Constant Flow Field: This case used an aquifer with the following geohydrologic and model parameters: aquifer thickness, b Darcy Velocity, v Porosity, n Solute Mass/Unit Thickness Total Mass Injected Mass/Particle, M Particles Times Dmax Zmax Longitudinal Dispersivity, aL Transverse Dispersivity, ayNo Retardation No Decay Number of Rows (Y dimension) Row Spacing Number of Columns (X dimension) Column Spacing

32.81 ft 6.56 ft/day 0.35 2.35 lb/ft 77.1 lb 0.03281 lb/particle 2,350 3.96 days 10.59 days 16.59 days 3ft 0.3 ft 13.12 ft 3.28 ft 19 16.4 ft 40 16.4 ft

The source of contamination is a slug source along a vertical line that is located at X = 57.4 ft, Y = 156 ft and is throughout the second aquifer layer (32.81 ft). Figures 25, 26, and 27 show the RAND3D, RAND2D, and the analytic solutions for this case at three different times: 3.96, 10.59, and 16.59 days. The three-dimensional solution agrees well with the analytic solution as well as the two-dimensional solution. There appears to be slightly more deviation from the analytical solution at the early times (3.96 days) than for the 10.59 and 16.59 days. For short time periods, the discreteness of the model will be more evident; therefore, the results will deviate more. However, as the simulation time increases, the discrete particles will be smoother, and there will be less variation.


57

ModdPnmctm: 3000 Particle* 29.121hi/pirtkk Din«" 10

Ceotetic Pmnekn: Pwottcy.R-QJS

BL-30 feet *T" 5 fee) az- «fed

First Run 12 May 1993

Concentration Comottn (ppm) at Day 2800 Double Aquifer System Top Layer 110 TeeC thick (Duty VclociXy - 0.525 ft/day) Bottom Layer 5 feet thick (Duty Velocity - 0.0 ri/y) Cootniueut Sinxlc Source in lop Layer at (500,900)

Figure 23.

Comparison of solution technique, Run 1 concentration contours

Model Parameters: SOOOfaitkki 29.l2H«/pwtfck Dm» «10 Zstax- 1

Geolojk Pararoetcrt: Pocotity. a * 0.35 OL"30f«i By- 5 feet az- Ofeet

Second Run 12 May 1993

Conccntralioo Contours (ppm) at Day 2800 Double Aquifer System Top Layer 110 feel thick (Dircy Velocity - 0.525 ft/diy) Bottom Layer 5 feet thick (Darcy Velocity - 0.0 ft/day) Conttnuoui Single Source in Top Layer at (500.900)


58 Chapter 4 Models Description

Concentration Levels for a Slug Source in a Constant Velocity Field Simulation Time 3.96 Davs :

|

!

i

i

25 20

i

»I

15

o U

1

1

Tf~ \

1 1 :

——•—■ 3D 0"—

2D - Analytic

i

10'

f

\

i

■

"—i

200

300

500


Figure 25.

Simulation of a slug source, Case 2 at time 3.96 days

Concentration Levels for a Slug Source in a Constant Velocity Field Simulation Time 10.59 Days

30

25

sa.

a. c o

3D 2D Analytic

20 15 10

U

400

500

600


Figure 26.

Simulation of a slug source, Case 2 at time 10.59 days


59

Concentration Levels for a Slug Source in a Constant Velocity Field Simulation Time 16.59 Days 30

25

c c c

20

15

a «j o c o U

10

0 ^/wja* '^^sJIWS^i®iwS

^^^"■O'loO-»

100

200

300

400

500

600


Figure 27.

Simulation of a slug source, Case 2 at time 16.59 days Case 3, Continuous Source in a Radial Flow Field: This case used an aquifer with the following geohydrologic and model parameters: aquifer thickness, b Inflow, Q Porosity, n Total Mass Injected Mass/Particle, M Particles Times Dmax Zmax Longitudinal Dispersivity, o^ Transverse Dispersivity, ar No Retardation No Decay Number of Rows (Y dimension) Row Spacing Number of Columns (X dimension) Column Spacing

32.81 ft 882.83 ft3/day 6,610 gal/day 0.25 200 lb 0.8 lb/particle 10,000 20 days 40 days 0.6 ft 0.06 ft 0.984, 0.492, 0.049 ft 0.246,0.123,0.012 ft 39 3.28 ft 39 3.28 ft

This case provided a problem not encountered in the previous cases. The velocities in the computational grid were determined by the inflow rate (g) and the distance from the well. The formula used for the velocity magnitude was:

60


V=Q/A

(27)

where Ö = inflow, 882.83 ft3/day A - area of a cylinder defined by A = 2nRb R = distance from well b = aquifer thickness, 32.81 ft The solution is acceptable for all the locations except at the well itself. Since the velocity magnitude is inversely proportional to R, as R —> 0, V —> oo. Therefore, velocities near the injection well will be interpolated using extremely high values. To avoid this, one can either set the velocity at the well to 0 or set the radius at a distance so that all particles start with reasonable velocity values. If the velocity at the source were set to 0, then the program crashes. This is because the dispersion term depends on the velocity. This meant that the source could not be a line (as in the previous two cases). The only way to run this case was with the source defined as a cylinder with its center at X = 63.96, Y = 63.96, and a cylinder height equal to 32.81 ft. Figure 28 illustrates the location and size of the cylinder and also the velocity magnitudes. The radius of the cylinder (well radius) had to exceed 4.64 ft in order to avoid the velocity interpolation routines use of the velocity at the well. The method in which RAND3D distributes the particles around the cylinder is supposed to be in a uniform pattern. The results, shown in Figures 29-34, indicate that there might be a problem in the routine that determines the particles starting point. The solution is not symmetric. These results cannot be accounted for even if the assumption is made that there will be a certain lack of symmetry due to the random nature of the solution. The problem could be with the routine that determines the particle starting points or with the random number generator of the computer. It should be noted that in the original test case for the two-dimensional model, the transverse dispersivity, aT, was set to 0. When RAND3D is run with this value, every particle travels in a straight line away from the source. It was decided to use a value of a^ = a^/4 in order to get results that made sense. However, even with the highest values of aT and aL, the asymmetry exists in the results. Comparison with the two-dimensional and analytic results would be meaningless, as they would depend on values along an undefined line through the center that could be chosen to give any degree of agreement. Summary. Once a user becomes familiar with RAND3D, it is fairly easy to run. It is also fairly easy to enter erroneous input parameters, like any other codes, and in some cases, one must let the program finish a simulation; it can be corrected. When particles reach the model boundary, they "bounce" back. Extending the boundaries helps in avoiding the "bounce" back; this requires either increasing the row or column spacing or the number of rows or columns. Such modifications can affect the resolution and/or execution time.


61

The user may even need to recompile with larger dimensions in the arrays, in which case he would need to have Microsoft Quick BASIC compiler. The code is limited to use on IBM-PCs or compatibles. This limits the size to 640 K. For large complex problems requiring long simulation times and many particles, using PCs may also be inconvenient. A lot of the limitations are probably addressed in the code's recent release. Multiple time simulations of continuous sources runs require that the simulations start at time 0. You must also reinitialize the particles, or they will start where they were at the end of the last time simulation (resetting the time to 0 does not reset the particles to their original locations). Truly complex problems, with many layers with different geohydrologic parameters are not easy to run with RAND3D. It allows only single porosity and dispersivity values throughout the domain. In addition, if there are cells with no velocity, particles that enter will never leave that cell. Saving data requires you to define a constant x-y increment and number of rows. This requirement is not very useful since a grid has already been defined. In fact, if your computational grid has a Ax * Ay, you must define an increment that is at least as large as the largest of the grid increments. This means that you smooth some of the results. Modeling large remediation projects with this model would be very time-consuming for the untrained user. Modifications to take care of some concerns mentioned above would make RAND3D more useful. A new version of RAND3D was recently released that may address some of the weaknesses.

Unsaturated Flow and/or Transport Models UNSAT1

The model UNS ATI is a one-dimensional finite element model for variably saturated soil profiles. It is distributed by the International Ground Water Modeling Center (IGWMC) located in Golden, CO. The current model being distributed is Version 1.0 and was written by M. Th. van Genuchten. The IGWMC charges a nominal fee for the software to cover the costs of distributing the program and documentation. The UNS ATI model can be obtained by writing to the following: IGWMC Institute for Ground-Water Research & Education Golden, Colorado 80401-1887, USA Phone: (303) 273-3103 The UNSAT1 model is a generalized Hermitian finite element computer model. It can be used to simulate variably saturated moisture movement in one dimension. Furthermore, the model can be applied to both 62


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Concentration Contours (ppb) at Day 40 Double Aquifer System Constant Radial Row Top Layer 31i feet laid: Bottom Layer 5 feet tWck (so (low) Conüauous Single Source la Top Layer at (63.96.63.96) Source Radius « 5 tea Inflow st Source »6610 gal/day

Figure 34.

Concentration contours, Case 3, Test 3 at Day 40

homogeneous and nonhomogeneous soil profiles, enabling the user to analyze moisture movement in soil profiles containing abrupt and smooth changing profiles. The UNSAT1 model was written in FORTRAN, and the currently executable file being distributed was compiled using Microsoft FORTRAN Version 3.2. The operation of UNSAT1 has the following run time requirements: • IBM-PC, XT, or AT • 512KRAM • DOS 2.0 or higher • Intel 8087 or 80287 Numerical Coprocessor • One floppy disk drive The model, as currently distributed by the IGWMC, includes both executable and source code files. The source code is supplied to permit users to alter the program to meet specific programming needs not handled in the distributed version of UNS ATI and for modification of the BC 66


(boundary conditions) subroutine and SPR (soil property) function. The BC subroutine and SPR function are problem dependent and must be modified for user-defined data sets. The BC subroutine defines the transient boundary condition at the soil surface, and the SPR function calculates soil hydraulic properties. In general, most UNSAT1 applications require input data set creation and BC and SPR modification. Modifying the UNSAT 1 program will require the use of a FORTRAN compiler, which is not provided by IGWMC. Other files that are supplied include an input and output data set and a postprocessor program. The postprocessor program can be used to remove carriage controls from the output data set. In addition, a software product description detailing model application is included. Notices describing changes in the original source code of UNS ATI are provided by IGWMC, which maintains a list of licensed users. Overview. The computer model UNSAT1 was written to allow for simulation of moisture movement in a one-dimensional variably saturated soil profile. The soil profile can be nonhomogeneous, permitting a variety of soil properties. Currently the model only simulates moisture movement and not chemical transport. Files distributed from the IGWMC include UNS ATI.FOR, UNSAT1.EXE, UNSAT1.DAT, UNSATl.OUT, STRIP.FOR, STRIP.EXE, and UNSAT1.DOC. The FORTRAN source code for UNSAT1 is listed in the UNS ATI.FOR file. The compiled version of this code is the UNSAT1.EXE file. It was compiled using Version 3.2 of Microsoft FORTRAN. The program can be tested by running the example data set UNSAT1.DAT and then comparing the generated output data set to the file UNSATl.OUT. The two output files should be identical. Carriage controls can be removed from the output data set by using the STRIP.EXE program. The STRIP.FOR is the source code for the executable file, and cleans up the output data set by executing the carriage control commands. Finally, UNSAT1.DOC contains the information required to run the program as well as a description of the software product. The UNS ATI program was developed using a Galerkin finite element technique to solve the variably saturated flow equation. A series of basis or shape functions were used to approximate the dependent variables, pressure head or moisture content. First-order continuous cubic (Hermitian) polynomials were used as the basic functions for the one-dimensional, variably saturated flow equation. Input/output parameters. Operation of the UNSAT1 model requires a single input data set and the executable file UNSAT1.EXE. Upon typing the command UNS ATI, the user will be prompted for the names of the output file name (unit 6) and input file name (unit 5). The supplied input file, UNSAT1.DAT, should be used for the first run to ensure that the model is operating correctly. Any output file name can be used. After the run, the output file created should be compared with the UNSATl.OUT file to verify the run. The output files should be identical. The compiled version of UNSAT1.EXE is for example problem 2 in the user manual. The moisture model used for this problem and the UNSAT1 program is based on equations developed by van Genuchten (1978). The equations require information pertaining to soil hydraulic properties. The Chapter 4 Models Description

67

distributed version of UNSAT1.EXE uses soil hydraulic properties for the soil layers of problem 2. Again, for user-specified problems, the subroutine BC and function SPR must be modified. These files contain information relating to boundary conditions and soil hydraulic properties. After alteration, a new UNSAT1.EXE file needs to be created by compiling the usermodified version of the UNS ATI.FOR file. The input data set for the UNS ATI model follows the FORTRAN 77 format statements. Table A2 in the users manual provides the information regarding the format structure for each column entry. Descriptions of the variables contained in the file are further described in Table Al. Information contained in the input file includes global parameters, time steps, boundary and initial conditions, and soil properties. New input files can be created be modifying the distributed input data set or by creating a new one following the structure outlined in Table A2. The output data are written to the file specified by the user as "unit 6" when running the program. The output file contains descriptions of the input parameters, surface moisture values, initial conditions, and soil hydraulic properties. Following this information, the pressure head and moisture contents are given for each depth (node) at each time interval specified by the user in the input data set. This information can then be used to graph pressure distributions produced during the simulation. The output data set produced when running UNS ATI is given in Table A4 in the manual. Following the computer run, the user can then use the STRIP.EXE postprocessor program. This program removes or executes the FORTRAN carriage controls from the UNS AT LOUT or output file. The program will prompt the user for the file created upon running the UNSAT1.EXE program, and a new name must be assigned to the file created using the strip program. The STRIREXE program will overwrite the original input data set if that file name is used. The output from the simulation can be sent directly to a printer by specifying unit 6 as the local printer (lpt1). Evaluation. The author reported run times of approximately 25 min. However, the type of machine it was run on was not mentioned; thus, direct comparisons cannot be made. The time for a run will vary based on factors such as number of soil layers, time intervals, and the computer used. For example, running the same example data set on a Gateway 2000 4DX2-66V microcomputer (486-66 MHz) took only 25 sec as compared with the 25 min reported in the documentation. Summary. The example data set supplied with the model ran without difficulty. The output file created running the program matched the output file provided with the documentation indicating a successful simulation. Moisture content profiles created using output from the simulation produced graphs that were reasonable and within physical expectations for a moisture model. The input data sets for the UNS ATI model are rather difficult to set up; thus, the model could be greatly enhanced with a preprocessor to aid in the creation of input files. Currently, the input data sets are either created from scratch or by editing an existing input file. The tendency for mistakes creating these files is great. Any extra character outside of the format 68


field will create errors terminating the program. The program does not give clues regarding the location of the error in the input data set, and much time can be lost searching for mistakes. A preprocessor could create these input files, reducing the time and effort required in the structuring of input data sets. The UNS ATI model can be used to simulate moisture movement in a one-dimensional, saturated-unsaturated, homogeneous-nonhomogeneous soil profile. The model does not handle contaminant transport. However, the output from the model can be used to provide moisture profiles, which could then be used as input for a contaminant transport model.

CHEMFLO CHEMFLO is a software system designed to define, solve, and display the water and chemical movement in the unsaturated or vadose zone. The system was developed for the Robert S. Kerr Environmental Research Laboratory (Nofziger et al. 1989). The software system is intended as both a teaching tool and a decision-making tool. The software system was developed for the PC environment. The model requires 640K of RAM to run and needs the ansi.sys device driver loaded in order for the screens to be legible. The software system was evaluated on a 486/66MHz IBM PC compatible computer. The software/ hardware requirements to run the software system are as follows: • IBM PC, AT, PS2, 386 or 486 compatible microcomputer. • MS-DOS or PC-DOS Version 2.01 or higher. • 640K base memory. • Two floppy disk drives or one floppy disk drive and one fixed disk. • An 80X87 math coprocessor is highly recommended. The software system consists of a pair of partial differential equations to solve for water and chemical movement. The water flow is described using Richard's equation to solve the one-dimensional water movement in unsaturated soils. Chemical movement, sorption, and degradation are described by solving the convection dispersion equation. The two equations are solved numerically using finite difference. The major model assumptions include homogeneous soil properties, instantaneous and reversible chemical partitioning, first-order degradation rate in both the liquid and solid phases, zero-order degradation rate constant for the liquid phase, and negligible hysteresis in the wetting and drying processes. The model can simulate both drainage and desiccation of a soil. Four soils are included in the soil database, a part of the software system. The soil database can be easily modified to include other soils and their properties. Input/output parameters. The model requires input parameters defining the soil conditions, the chemical properties and characteristics, and the water system. Boundary conditions for water flow may be defined at Chapter 4 Models Description

69

the upper and lower soil surfaces. Three types of boundary conditions can be applied at the soil surfaces. At the upper and lower surfaces, the boundary conditions can be specified as constant potential, constant flux, and mixed type. In addition, a fourth boundary condition, called the rainfall boundary condition, can be applied at the upper soil surface. The program allows the user to select one of several moisture-retention models like Brooks-Corey, van Genuchten, Haverkamp, and Brutsaert. Analogous models are available to describe the hydraulic conductivitymoisture content relationships. The user must provide the coefficients used to fit the moisture retention models. The four soils included in the soil database have "typical" coefficients that could help the user in selecting appropriate coefficients. However, the coefficients used in these moisture-retention models should be fitted from field data if available, since the coefficients range is significant. Two types of boundary conditions for chemical simulation can be specified at the soil surface. Constant chemical concentration in the inflowing solution may be specified. A constant concentration at the soil surface may be specified. That is, the concentration at the upper surface is held constant over time. Initial chemical concentration in the soil column may vary with depth. Output from CHEMFLO may be in both graphical and tabular form. Graphical displays include matric potential, conductivity, saturation, flux density, and driving force with depth and/or time. The user can select from a variety of graphs for screen displays and tabular output. Runs can be saved into "simulation" files; the tabular output, if selected, then takes the same name with the TAB ending (i.e., "filename.TAB"). The size of the tabular output can be significant. Attention to both the time step and the tabular output time step is needed. Equations. The partial differential equation used to describe onedimensional water movement is that of Richards (Nofziger et al. 1989): dödh dh dt

=

d_ tf(A)| ^ - cos(A) dz

(28)

where h = h(z,i) = matric potential z = distance coordinate parallel to flow direction t = time cos (A) = cosine of angle between direction of flow and vertical downward direction K(h) = hydraulic conductivity as a function of matric potential 9 = volumetric water content The system can simulate water movement in either a finite length soil column with uniform or nonuniform conditions, or in a semi-infinite soil

70


column with uniform initial conditions. For the finite soil column of length L, the initial condition is: h(z,t) = h(z,0) for t = 0 and

0 < z < L

(29)

Four types of boundary conditions can be employed at the surface of the soil column: constant potential, constant flux, mixed type boundary, and rainfall. The rainfall boundary condition is a specific case of the mixed type boundary where the flux equals to the rainfall rate and the matric potential at the top of the column equals zero. For the finite soil system, the same boundary condition choices are available at the lower boundary except for the rainfall boundary condition. Movement and degradation of contaminants are simulated using the convection-dispersion equation:

—(GC + pS) = -^-\ 0D ^- - qC - XfiC - yxpS + X0Q at dz\ ydz ))

(30)

where C = contaminant concentration dissolved or liquid phase 5 = concentration of contaminant in solid phase D = dispersion coefficient q = flux of water p = soil bulk density %l = first order decay in liquid phase Yj = first order decay in solid phase XQ

= zero order decay constant in liquid phase

Assuming instantaneous equilibrium adsorption and linear partitioning, S = KC, where K is the linear partition coefficient. Incorporating linear partitioning into Equation 30 yields: d_

(eRC) = — Oof-^ - qC] -(XjG + YlPK)C + X00

dt'

(31)

where R = 1 + pic/0 is the retardation factor for the contaminant in the soil column. CHEMFLO solves Equation 30 coupled with Equation 28 to obtain the dissolved contaminant. The particulate contaminant is estimated from the instantaneous equilibrium adsorption relationship. Evaluation. The code was able to solve the example cases contained in the database. The example cases demonstrate the capabilities of CHEMFLO and allow the user to apply the different moisture-retention models. The soils database was useful in finding ranges for the fitted parameters of the different soil-moisture models. Though the model is user friendly and fairly fast in solving some typical soil-moisture problems, it can be very slow in solving problems where the moisture content of the Chapter 4 Models Description

71

soil is very small. The time steps required to achieve converging solutions can be as small as 10 hr, where dry conditions exist. The model was evaluated against the Prill, Johnson, and Morris (1965) experimental column drainage data. The Fresno medium sand fitted parameters were estimated (Figures 7 and 8) using van Genuchten's and Haverkamp's moisture-retention models. Figure 35 shows the water movement simulation against the experimental data. The model performance at the early time periods (1,2, and 4 hr) are not as good as the later periods (16, 75, and 96 hr). Overall, the model results compared favorable with UNS ATI and SUTRA, while the input data required were much less than that required by SUTRA and UNS ATI. Figures 36 and 37 show sensitivity analysis on both saturated hydraulic conductivity and time step, respectively. The effect of the time step was not as critical since the largest time step, 1 10 , was small enough for a stable and converging solution. A smaller time step, 1 10"5, did not improve the simulation. The saturated hydraulic conductivity did not show major effects with changes in the hydraulic conductivity of less than 50 percent (Figure 36).

Moisture Distribution

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Summary. The CHEMFLO system is very useful and powerful; the model did a very credible job of simulating water movement through a soil column. The software is user friendly, the user's guide is well documented, and the model equations, boundary conditions, as well as the limitations are presented in the documentation. The system is a great teaching and screening tool for fate and transport of contaminants in the vadose (unsaturated zone). CHEMFLO is an appropriate tool when a site has limited amount of data. The model can be used to assist in the application of more complex two- or three-dimensional unsaturated and or coupled ground water models. Further, CHEMFLO evaluation with data from either a transport experiment or a hypothetical scenario is recommended. 72


Moisture Distribution Fresno Medium Sand Effect of Saturated Hydraulic Conductivity

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One setback is that the system is distributed as a PC executable; thus, no source code is available with the distribution disk. The transfer of the graphical screens from the display to an attached laser printer did not work. The software Pizzazz Plus was used to capture the screen display and transfer them to the laser printer. Other public domain screen capture programs will probably perform as satisfactorily as Pizazz Plus. Chapter 4 Models Description

73

PRZM-2

The Pesticide Root Zone Model, PRZM-2, was developed as a tool for predicting pesticide fate in the crop root and unsaturated zone. The model is supported, updated, and distributed by the Center for Exposure Assessment Modeling (CEAM) at the U.S. EPA Environmental Research Laboratory located in Athens, GA. The model can be obtained free of charge from CEAM's electronic Bulletin Board System (BBS) or by sending the appropriate number of diskettes to CEAM. Obtain information regarding these procedures by telephoning CEAM at (706) 546-3549 or by writing to the following address: Model Distribution Coordinator Center for Exposure Assessment Modeling Environmental Research Laboratory U.S. Environmental Protection Agency 960 College Station Road Athens, GA 30606-2720 The PRZM-2 model was originally developed and tested on a Digital Equipment Corporation (DEC) VAX 6310 using VAX VMS FORTRAN-77. The current distribution version of PRZM-2 was built using the Lahey FORTRAN (F77L-EM/32) extended mode FORTRAN compiler Version 5.01. The operation of the PRZM-2 model has the following run time requirements: • 386 or 486 compatible microcomputer • MS or PC DOS version 3.30 or higher • 640K base memory • 4 MB of extended (XMS) memory • 4.5 mb free hard disk storage The PRZM-2 model can also be run on other computers. It has been run on a PRIME 50 Series minicomputer running under PRIMOS, the SUN SPARC station running under UNIX/SUNOS, and the IBM PS/2 Model 8085-071. The model comes complete with an executable file, the FORTRAN source code files, and the make files required to compile, link, and run the task image file PRZM2.EXE. The model does not include a text editor or FORTRAN development tools that would be required to modify the source code for specific applications. User-modified versions of PRZM-2 are not supported by the CEAM. Most applications of the PRZM-2 model will not require program modification. Thus, the user will only need to set up the appropriate input and output data files and run the PRZM2.EXE program. Overview. PRZM-2 is a management tool that was written to evaluate the effects of the application of pesticides applied for agricultural purposes on water quality. The model is capable of determining the fate of chemicals as they migrate through the crop root and vadose zone. It is also capable of simulating the effects of multiple pesticides and can perform basic exposure assessments. The model was developed at the Environmental Research Laboratory in Athens, GA. 74


A one-dimensional, dynamic, continuous compartmental model, PRZM-2 was developed by modifying PRZM, Version 1. The modifications to PRZM-1 were necessary to improve the hydrology, soil hydraulics, and solution techniques for the transport equation and to add a stochastic component to the model. One improvement that was made was the addition of the Vadose Zone Flow and Transport Model (VADOFT) module, written to handle flow and transport through the unsaturated zone. Unlike PRZM1, which assumes the soil drains to field capacity following the addition of water into the root zone, VADOFT allows for variable moisture contents. Thus, in areas where drainage is restricted, PRZM-2 with VADOFT will produce a more realistic simulation than PRZM-1. The PRZM-2 model can be run with or without VADOFT. The model consists of four main modules: EXESUP, PRZM, VADOFT, and MONTE CARLO. The first of these, EXESUP, is the module that controls the simulation. The user can specify whether or not to run PRZM, VADOFT, or MONTE CARLO for a particular run. The PRZM module controls transport and transformation simulations for the root zone. This module can be run for the entire unsaturated zone if the soil type is one that typically drains to field capacity rapidly following storm events. VADOFT performs transport and transformation simulations for the vadose zone. This is the option that should be used for soils with low hydraulic conductivity values. The last module, MONTE CARLO, if selected will provide the user with uncertainty or risk assessments. This module will provide probabilistic estimates of exposure concentrations by taking into account the variability encountered in natural systems and the uncertainty in system properties and processes. The two major computational modules are PRZM and VADOFT. PRZM provides pollutant fate calculations for the root zone and has the capacity to incorporate the effects of various management practices, and VADOFT is used to calculate transport and fate of the chemicals within the vadose zone. Both of these modules are used for one-dimensional transport. The modules are connected by the use of bridging algorithms that conserve water and solute mass. Input/output parameters. The operation of the PRZM-2 program requires several input files. The input files include a meteorological file (MET.INP), an execution supervisor file (PRZM2.RUN), a PRZM input file (PRZM.INP), a VADOFT input file (VADOFT.INP), and a MONTE CARLO input file (MC.INP). The first two files, MET.INP and PRZM2.RUN, are required for each run. The other three, PRZM.INP, VADOFT.INP, and MC.INP, are only required if they have been specified as being "on" in the execution file. Of course, at least one of the three must be "on" for the program to run. After a run has been completed, the output file PRZM.OUT is created, and the user can find the information requested for the run in this file. Other files that are created are TIMES.OUT and VADF.OUT. The TIMES.OUT file gives the output information for the time series data requested, and VADOFT. OUT presents simulation times and summaries of cumulative flow and concentration values. The names of the input, output, and scratch files can be changed by editing the PRZM2.RUN file. A chapter in the PRZM-2 user manual entitled "Parameter Estimation" was written to aid users in estimating input parameters required to run the model. The chapter is well written and includes aid in determining input records for EXESUP, PRZM, and VADOFT modules. By no means does Chapter 4 Models Description

75

the chapter provide all possible values for all parameters. It does, however, provide a starting place for these values as well as possible sources of reference. The PRZM-2 manual also provides error messages and warning codes, a variable glossary, and PRZM and VADOFT example input files in the appendixes. The input files are ASCII files following FORTRAN77 format structure. Each input file consists of several file records. The specific format statements for each record are given in Chapter 4 of the PRZM-2 manual. The manual lists the format parameters for the meteorological (MET.INP), execution supervisor (PRZM2.RUN), PRZM (PRZM.INP), VADOFT (VADF.INP), and MONTE CARLO (MC.INP) input files. The meteorological file, MET.INP, consists of weather data to be used in the run. It includes information on daily precipitation, pan evaporation, temperature, wind speed, and solar radiation. The global parameters are specified in the PRZM2.RUN file. The information contained within this file specifies the desired modules for the simulation, number of zones to simulate, input and output file names, starting and ending simulation dates, number of chemicals to simulate, weighing parameters between PRZM and VADOFT, and echo and trace levels during execution. Without the meteorological and execution supervisor files, the PRZM-2 program will not run. The PRZM, VADOFT, and MONTE CARLO input files also consist of formatted records. Each of these input files can be turned "on" or "off as specified in the PRZM2.RUN file. If a file is turned "on," then it must be defined. Otherwise, it can be omitted. The exception is the VADOFT module; it must be included whenever the vadose zone transport simulation is turned "on" as well as when it is turned "off." A complete description of these input files, as well as the format statements for each file record, can be found in Chapter 4 of the PRZM-2 users manual. These input files are also well documented in the manual. The user can specify the output frequency. A selection can be made for either daily, monthly, or annual summaries. Predictions in the model are made on a daily basis. Thus, daily time series values for the specified fluxes and storages can be written to sequential files. An additional feature in PRZM-2 is the ability to specify a SNAPSHOT. The SNAPSHOT feature allows the user to obtain the pesticide concentration for each soil compartment at user-specified times during the simulation period. Thus, even if the user has selected monthly or annual output, concentration profiles can still be obtained for any desired day during the run using the SNAPSHOT feature. There is no limit on the number of SNAPSHOTS that can be taken during a simulation. As previously mentioned, the output file names can be selected by the user in the PRZM2.RUN file. Typically, four output files are created during a simulation: PRZM.OUT, TIMES.OUT, VADOFT.OUT, and MC.OUT. Additional output files created are RESTART.PZM, VFLOW.RST, and VTRANS.RST. These files are used to restart the simulation at the previous simulation termination point. This allows continuation of a simulation without having to repeat the initial run.

76


The PRZM.OUT file contains information pertaining to both the input and run information. The file first lists the input data used for the run and includes the simulation start and end dates, hydrology and sediment related properties, soil and erosion parameters, crop information, pesticide properties, and soil-horizon data. Basically, this is a tabular summary of all input data. Next, the output that was selected in the PRZM.INP file is given. This can include hydrologic, pesticide flux, and pesticide concentration data in either daily, monthly, or annual form. The TIMES.OUT file contains the time series data for selected parameters. The specific times that data are printed in this file were selected by the user in the PRZM.INP file. A maximum of seven time series plots can be made for each run. Flow and transport output data from the VADOFT module can be found in the VADF.OUT file. This file contains cumulative volumetric storage, inflow volume, outflow volume, mass storage, mass decay, inflow mass, and outflow mass. Once again, the data are printed out at daily, monthly, or annual intervals as specified by the user. Even if a daily or monthly output is selected, the file will still print out annual summaries of cumulative concentration at the end of the file. The MC.OUT file contains information regarding the input and run data. The input data are printed as a summary for the MONTE CARLO run. This includes the number of input parameters being varied, confidence level, and statistical description of each parameter distribution. The output is given as a flux for each chemical based on the statistical description entered by the user. Evaluation. The current documentation of PRZM-2 has several example files that can be used to test the program. The examples that are given include both input, output, and the execution supervisor files. Two years of weather data are available in the example meteorological input data file (MC.INP). Therefore, the maximum simulation time is limited to 2 years with the example file. The files that are included enable the user to test all three components (PRZM, VADOFT, and MONTE CARLO modules) of the PRZM-2 model. The modules can be run simultaneously or independently. The time required to run the PRZM-2 program is dependent upon the computer used and the number of modules being run in the program. For example, using a Gateway 2000 4DX2-66V microcomputer (486-66MHz), a time of 7.18 min was recorded running all of the modules simultaneously for the example data set over a 2-year period. However, a time of only 32.79 sec was recorded running the same data set using only the PRZM module. Other factors that affect the run time are the number of years, chemicals, irrigations, horizons, and modules used for the simulation. Using the microcomputer, all of the PRZM-2 example files were run in less than 10 min. While the program is running, the user is provided with a simulation status report that indicates the current step the program is calculating and the percent of the run that is complete. The example data sets supplied with the PRZM-2 program all run correctly without modifications to the files other than the PRZM2.RUN file, which determines the global parameters for each run. Summary. The PRZM-2 model can be used to simulate pesticide migration through the saturated-unsaturated soil profile in one dimension. The addition of the VADOFT module allows for application of the model to depths greater than that of the crop root zone. After running the example Chapter 4 Models Description

77

data sets, the model was able to produce results consistent with physical expectations. The documentation for PRZM-2 is well written, and the model is maintained by the CEAM. A preprocessor should be added to the model to aid in the creation of input data sets. Currently, the best way to create new input files is to edit the ones that are shipped as examples with the current model. This is a time-consuming process. Also, any characters typed outside of the format field result in errors. Thus, great care must be taken when creating new input files. A preprocessor would enhance the model by providing a better way of creating input files. The PRZM-2 model is a one-dimensional model and should not be used for field situations such as fields exhibiting a high degree of lateral flow, requiring a two- or three-dimensional model. This may occur in sloping fields with sand over dense clay layers. In such a field, the tendency will be for the water to move laterally as it accumulates at the top of the clay layers. A twodimensional model allowing for lateral flow would be better suited for this situation than PRZM-2. Selection of the right model is critical in obtaining meaningful results. A good application of PRZM-2 would be in estimating potential pesticide leaching through the vadose zone.

Coupled Unsaturated/Saturated Flow and/or Transport Models FEMWATER

FEMWATER is a full three-dimensional (3-D) finite element method (FEM) program that models a time-dependent saturated/unsaturated flow of water in porous media. A steady-state solution can also be efficiently obtained as the program has a separate section for this task. Features include the following: a. Heterogeneity. Heterogeneous geologic formations are handled by assigning different hydrogeologic parameters to groups of elements. b. Anisotropy. A full 3 by 3 hydraulic conductivity tensor can be used to model anisotrophy. c. Initial conditions. Initial conditions can be prescribed or obtained from the steady-state solution. d. Boundary conditions. A wide variety of time-dependent boundary conditions are available, including specified head, specified flow, sources and sinks, precipitation and evaporation with ponding options, and automatic time step resetting with sharply varying boundary conditions. e. Unsaturated flow curves. Pressure head, saturation, relative hydraulic conductivity, and water capacity curves for unsaturated flow can be input in tabular form or computed with analytic functions. 78


/.

Multiple blocks. A multiblock definition of the grid and solution of the equations is allowed.

g. Mass balance. A mass balance computation over the entire region is done at each time step. Equations. The governing partial differential equation used in FEMWATER is Richard's Equation

V*[krks»(Vh + Vz)J + q = Fj-

(32)

where lcr = relative hydraulic conductivity ks = saturated hydraulic conductivity tensor h = pressure head q = source or sink t = time F = water capacity given by

ah where 9 is the moisture content. In the saturated zone, F is very small (set to zero in FEMWATER), 9 becomes the porosity, and kr = 1. Otherwise, F, 9, and kr are functions of h, making Equation 32 nonlinear. Evaluation. The performance of the model will now be given. The example problems provided with the documentation were first tested to determine if computed results matched that in the documentation. Results obtained for all three example problems were the same as the output given in the documentation. Three analytical solutions were tested against FEMWATER as discussed below. 1-D vertical flow without gravity. The problem consists of unsaturated vertical flow in a column of sand where the gravity option has been turned off. The problem can also be considered as horizontal flow from one boundary to another. The grid is the same as that given in FEMWATER's documentation (Yeh and Cheng 1994) for the first problem. Each element is 5 m high, giving 164 nodes and 40 elements. Two runs were made with the first being 200 time steps at At = 0.05 day and the second run being for 20 time steps with At = 0.5 day. When the time step is very small, the differences between analytical and computed pressure heads remain stable. However, a large At causes a gradual degeneration of results. The first run with 200 time steps took 4 min 48 sec on the Silicon Graphics 4D/320 VGX workstation, and the second run with 20 time steps took 53 sec. The Silicon Graphics 4D/320 VGX runs approximately four times faster than a 486/33MHz PC.


79

1-D vertical flow with gravity. This problem is very similar to the first problem, except this time the gravity option has been turned on, and the equation for relative hydraulic conductivity has been changed. The grid is the same as that of the first problem, and, as before, At = 0.05 day with 200 time steps. The comparison of analytical and computed pressure heads were again reasonable. However, a gradual loss of symmetry occurred in this example when the tolerance was set at 0.02 but was remedied when it was set to 0.0002. This run with 200 time steps took 4 min 48 sec on the Silicon Graphics 4D/320 VGX workstation. 3-D steady-state flow. This problem consists of steady-state flow in a rectangular region of sand surrounded by clay. Both the sand and clay are initially at zero pressure, but then significant drying occurs on the top boundary of the sand such that now the pressure head is some negative value h0. The clay keeps the sand at zero pressure on the other boundaries throughout the time period of the analysis. As in the first problem, the gravity term is neglected. The grid is very similar to that given in FEMWATER's documentation for the third example problem. The grid is a rather coarse 21 by 9 by 11 structured grid with Ax = 50 m, Ay = 50 m, and Az = 50 m except for the last three layers in which Az = 40, 30, and 20 m, respectively. The computed pressure heads compared favorably to those determined analytically except where the boundary condition changes abruptly from h0 = -30 to 0 m, requiring a finer mesh in this area. This problem took 4 min. 8 sec. on the Silicon Graphics 4D/320 VGX workstation. Vauclin 's experiment. An experimental study of 2-D transient unsaturated/saturated flow with water table recharge was compared with results obtained from FEMWATER. The problem consists of flow in a homogeneous soil in a tank with an impervious bottom (see Figure 10). An influx of water is provided at the top of the tank with a pool elevation maintained at both side boundaries. The relative hydraulic conductivity versus pressure head curve was found experimentally to be kr =

-—w

(34)

A + (-hf

where A = 2.99 106, and B = 5.0. The moisture content equation was also determined experimentally to be e = e

*

a + TTJ (-h)p

(35)

where 85 = 0.30, a = 40.00, and ß = 2.90. Thus

aßH)^1

_ "

S

T

^2"

[a + (-hf]

„„ (36)

The grid consists of a 16 by 2 by 16 structured grid with the intervals slightly nonuniform to align with key points. The At was set to 0.05 hr and allowed to grow 20 percent per time step until a maximum At of 1 hr 80


was reached. Twenty time steps were run for a total of 8 hr. Because of the nature of the analytical curves of Equations 34-36, which become almost zero in certain regions, FEMWATER had trouble converging to a solution. This was remedied, however, by using the tabular option of the relative hydraulic conductivity, moisture content, and water-capacity curves with the water capacity curve not being allowed to drop lower than a small value of 0.001. Summary. FEMWATER does an acceptably good job of modeling saturated/unsaturated flow in porous media for the problems tested. Many needed basic features are available to the user, so it is recommended that this model be considered as a viable choice. However, the user may find the input data a bit tedious to prepare without additional tools, especially since this is a 3-D program. In fact, a graphical user interface with grid generation to help prepare the grid and postprocessor capability to visually analyze the results are essential for real-world applications. It is therefore recommended that this model be used in conjunction with such tools. A good choice is the Groundwater Modeling System (GMS) that is being developed for various models, including FEMWATER. Finally, it is recommended that the user select the tabular option for the curves describing the pressure-water content-relative permeability and that it be realized that for nonlinear problems some minor adjustments in the data may be necessary to achieve good results. The model's input, output parameters and documentation are summarized in Figure 38. FEMWATER Version

3-D EPA.

Language

FORTRAN 77.

Platform

486 PC or Unix workstation for small problems. Supercomputer for large problems.

Code

Complete source code provided in ASCII file on floppy disk.

Documentation

Complete report in WordPerfect 5.1 format on floppy disk.

input

Data file parly in fixed and partly in free-field format. Example problems available on floppy disk.

Output

Results are placed in files. Only information for selected time steps are output.

Memory Requirements

Varies depending on size of problem. Easily adjustable by changing PARAMETER statements in files.

Figure 38.


FEMWATER computer details

81

LEWASTE LEWASTE is a full 3-D hybrid Lagrangian-Eulerian finite element method (FEM) program that models time-dependent contaminant transport through saturated/unsaturated porous media. A steady-state solution can also be efficiently obtained, as the program has a separate section for this task. Features include the following: a. Heterogeneity. Heterogeneous geologic formations are handled by assigning different soil data to groups of elements. b. Anisotropy. A full 3 by 3 dispersion coefficient tensor can be used to model anisotropy. c. Adsorption. Linear isotherm, nonlinear Freundlich isotherm, and nonlinear Langmuir isotherm adsorption models are available. d. Initial conditions. Initial conditions can be prescribed or obtained from the steady-state solution. e. Boundary conditions. A wide variety of time-dependent boundary conditions are available, including specified concentration, specified flux of contaminant, sources and sinks, variable run-in/flow-out concentration profiles, and automatic time step resetting with sharply varying boundary conditions. /.

Multiple blocks. A multiblock definition of the grid and solution of the equations is allowed.

g. Mass balance. A mass balance over the entire region is computed at each time step. Equations. The governing partial differential equation used in LEWASTE is

e^- + pb^- + vvc = v«(e/)«vc) at

at

(37) - X(QC + pbS) + QCi» - QC where 9 = moisture content C = material concentration in aqueous phase {MIL3) pb = bulk density of medium (M/L3) S = material concentration in adsorbed phase (Af/Af) v = discharge velocity vector (Darcy Flux, LIT) D = dispersion coefficient tensor (L2/T) X = decay constant (\IT) Q = source rate of water Cin - material concentration in source

82


The linear isotherm model for adsorption is S = KdC

(38)

where Kj is the partition coefficient. The Langmuir nonlinear isotherm is (39)

1 + KC where Smax = maximum concentration allowed K = coefficient Finally, the Freundlich nonlinear isotherm is given by 5 = KCn

(40)

where n is the power index. The ij component of the dispersion coefficient tensor Dy is given by 11

e

v-v v v • ar|v|8« + {aL - aT) ' 7

D*x8 IJ

(41)

where aj = lateral dispersivity L = longitudinal dispersivity

a

Vf =

/ component of v

D* = molecular diffusion coefficient i = tortuosity 8,-,- = Kronecker delta tensor Evaluation. The example problems provided with the documentation were first tested to determine if computed results matched what was given. Results obtained for all three example problems were the same as the output given in the documentation. Two analytical solutions were tested against LEWASTE as discussed below. 2-D point source (Case 1). A pollutant is continuously injected into a relatively thin aquifer with enough vertical mixing occurring such that it can be treated as a 2-D problem. Water is flowing at a constant velocity in the +x direction. Also, due to symmetry, only the upper half of the problem needs to be solved. A grid of 51 by 11 by 2 was used with AJC = 50 m, Ay = 50 m, Az = 33.5 m, and At = 100 days (see Table 3 and Figure 4 for more details). Because of the form of the equations used in LEWASTE, the source rate of water g had to be made small and its input concentration Cin large with their overall product being the correct value


83

of

Qcin to properly model the analytical problem. With this, the results were quite good. Figure 39 shows a comparison of numerical and analytical results along the bottom of the grid away from the point source for / = 2,800 days. The run with 28 time steps took 20 min on the Silicon Graphics 4D/320 VGX workstation, which runs approximately four times faster than a 486 class PC running at 33 MHz.

Concentration

t - 2800 days Legend Analytical LEWASTE

1000

1500

2000

Distance (m)

Figure 39.

Comparison against analytic solution

3-D problem with time-varying boundary conditions. A full 3-D analytical solution was derived for a problem with time-varying boundary conditions. The problem consists of saturated flow in a rectangular region of sand that is initially clean until a spill occurs on the top of the sand. A concentration C0 in an s by s square area in the middle and on top of the sand is maintained for a time f0, and then it decays exponentially with a decay constant a. Water is flowing in the +x direction with a discharge velocity u. However, no contaminant due to dispersion flows to the boundary at x = a. Adsorption into the medium of bulk density pb occurs linearly with a distribution coefficient of Kd. The grid is a 21 by 21 by 11 rectangular mesh with Ax = 5, Ay = 5, and Az = 2. The At was first set to 1.0, and 20 time steps were run. The behavior of the solution was understood by looking at a single node through time. Figure 40 plots the numerical and analytical solutions for the time-varying problem. The model captures the trend but overestimates the concentration at the selected node. One explanation for this deviation is that the node selected was too close to the source; with a course grid, the numerical solution will tend to overestimate the concentration. A fine grid would reduce the amount of mass in the element and thus be closer to the analytic solution, which is a point solution. The run with 20 time steps took 1 hr 35 min on the Silicon Graphics 4D/320 VGX workstation. When the relaxation parameter was changed, only 58 min were needed for this run. 84 Chapter 4 Models Description

0.9 •, Legend

0.80.7 ______— c o

0.6

|

0.5-

8 o

O

0.40.3 0.20.10-

5

\

v_

10 Time

15

— Numerical — Analytical

20

Figure 40. Comparison against 3-D analytic solution Summary. LEWASTE does an acceptably good job of modeling contaminant transport in porous media for the problems tested. Many needed basic features are available to the user, so it is recommended that this model be considered as a viable choice. However, the user may find the input data a bit tedious to prepare without additional tools, especially since this is a 3-D program. In fact, a graphical user interface with grid generation to help prepare the grid and postprocessor capability to visually analyze the results is essential for real-world applications. It is therefore recommended that this model be used in conjunction with such tools. A good choice is the GMS that is being developed by WES for various models, including LEWASTE. Figure 41 shows the computer code details. LEWASTE Version

3-D EPA.

Language

FORTRAN 77.

Platform


Code

Complete source code provided in ASCII file on floppy disk.

Documentation


Input

Data file parly in fixed and partly in free-field format. Example problems available on floppy disk.

Output


Memory Requirements

Varies depending on size of problem. Easily adjustable by changing PARAMETER statements in files.

Figure 41.

Chapter 4 Moclels Description

LEWASTE features 85

SUTRA

SUTRA (Saturated-Unsaturated TRAnsport) is a computer program that simulates fluid movement and the transport of either energy or dissolved substances in the subsurface environment. Only the fluid movement and solute transport were evaluated under the current effort. The model was developed by the USGS and is distributed by the USGS, Geraghty and Miller, Inc. (G&M), International Ground Water Modeling Center (IGWMC), and Scientific Software Group. The version of SUTRA used in this evaluation was purchased from: Geraghty and Miller, Inc. Modeling Group 10700 Parkridge Boulevard Suite 600 Reston, VA 22091 (703) 758-1200 The current model being distributed by G&M is Version 2.0 and was written by C. I. Voss (1984). The USGS distributes the source code for either a nominal fee or free through the Internet and/or bulletin boards. The user is responsible for the compilation/linkage and execution in the PC environment. IGWMC, G&M, and Scientific Software Group charge a fee for the software to cover the costs of distribution, modification, implementation, and documentation. Some minor changes were incorporated into the computer code by the G&M staff to take advantage of the personal computer architecture and, in particular, Intel's 80386 CPU. The computer system requirements recommended by G&M are the following: • 80386 CPU • 80387 or equivalent math coprocessor • At least 1MB of extended memory (8MB recommended) • DOS version 3.3 or higher The computer model (SUTRA386), as distributed by G&M, includes three executables (1MB, 3MB, and 7MB), three example problems, two utilities to address and tune the personal computer's extended memory, and SUTIL. SUTIL is a utility program that creates XYZ text files compatible with SURFER and other contouring packages. SUTIL also provides a utility that generates portions of the finite-element mesh. Two types of finite-element mesh can be generated with SUTIL, radial and rectangular. The G&M version of SUTRA was selected because the developers maintain an accountable version of the original code and upgrades to the latest release (Version V-0690-2D) of the program. Shortly after finishing this evaluation, a new release of SUTRA (Version 2.0) became available to users. This review focuses on Version 1.0.

86


Overview. SUTRA employs a two-dimensional, hybrid finite element and integrated finite difference method to approximate the governing equations. SUTRA simulates fluid density-dependent saturated or unsaturated groundwater flow and either transport of a solute or transport of thermal energy in the groundwater. In simulating solute transport, the solute may be subject to equilibrium adsorption on the porous media, and both firstorder and zero-order production or degradation. SUTRA produces, as the primary calculated result, fluid pressures and either solute concentrations or temperatures, as they vary with time and space. The groundwater system may be either saturated, partly saturated, or completely unsaturated. Fluid density may be constant, or vary as a function of concentration or temperature. The single solute species can be conservative or undergo equilibrium sorption and decay/production. Three equilibrium sorption models are available in SUTRA, linear isotherm, Freundlich, and Langmuir isotherm. SUTRA's dispersion processes include diffusion and two velocity-dependent models: a velocity-dependent dispersion model for anisotropic media and a standard dispersion model for isotropic media. The isotropic model assumes direction-dependent values of longitudinal and transverse dispersivity. SUTRA is formulated in two spatial dimensions, and simulations can be run either in horizontal (areal) or vertical (cross-sectional) planes for saturated groundwater flow systems. Simulations for unsaturated flow modeling are carried out in the vertical plane; the same is true for variable-density fluid problems. Areal simulation of unsaturated flow and variable-density problems are usually physically unrealistic. In addition, either cylindrical or Cartesian (rectangular) coordinates can be selected. Although SUTRA is two dimensional, a three-dimensional quality is provided in that the thickness of the two-dimensional grid may vary from point to point. SUTRA is primarily intended for two-dimensional simulation of flow and either solute or energy transport in saturated variable-density systems (Voss 1984). The unsaturated capability of SUTRA was implemented because it is similar to nonlinearities encountered in density-dependent flow and transport problems. Thus unsaturated flow is provided as a convenience to the user, rather than as the primary application tool. SUTRA requires fine spatial and temporal discretization for unsaturated flow and thus is not an economical tool for extensive unsaturated flow modeling (Voss 1984). Simulations may be employed in one- or two-dimensional problems. Flow and transport simulation can be either steady state or transient. Steady-state solutions are often not appropriate for nonlinear problems (variable density, saturation viscosity, and nonlinear sorption). SUTRA uses a modular design; thus modifications and additions to the code are fairly straightforward. The design of the code has allowed the development of utilities such as preprocessors and postprocessors and mesh generators. In addition, the modular structure would ease the addition of nonequilibrium sorption, equilibrium chemical reactions, and chemical kinetics.


87

Input/output parameters. The pressure and water saturations are specified at each node in the problem domain to establish the initial conditions for the flow simulation. Two files, both ASCII and user-generated, provide the input for a SUTRA simulation. They are an initial condition file (pressure and/or concentration) and a mesh, properties, and simulation parameters file. In the input parameters file, the user can select flow, transport, flow and transport, or energy simulation. In addition, the user can select either saturated or coupled saturated-unsaturated flow simulations. The model has a restart option. The model does not have a preprocessor, although the version acquired from G&M included a postprocessor that creates an output file compatible with SURFER. Equations. Flow simulation in SUTRA is a calculation of how the amount of the fluid mass contained within the void spaces of the fluid matrix changes with time (Voss 1984). The flow equation solved by SUTRA is Equation 15. The fluid density is assumed to be a function of pressure (weak), temperature, and solute concentration. For solute transport, the concentration dependence is of the form: P = Po + |£(C - Cb)

(42)

For unsaturated flow, SUTRA requires a capillary-pressure saturation relationship to describe hydraulic conductivity and pressure saturation. The functions have to be supplied by the users; forms include those in Figures 2 and 3. The model includes the van Genuchten relationship. Solute transport is described by Equation 16. Since fluid properties are functions of solute concentration, an interactive approach is used within each time step to resolve the nonlinear coefficients in the fluid flow and solute transport equations. Numerical methods. SUTRA includes an optional numerical method based on asymmetric finite element weighing functions that results in "upstream weighing" of advective transport and unsaturated fluid flux terms (Voss 1984). In simulating transport problems, upstream weighing is generally discouraged. SUTRA numerical algorithms are not specialized for the nonlinearities of unsaturated flow. The model uses quadrilateral elements with four corner nodes to allow the simulation of irregular regions. Coefficients and material properties can vary throughout the mesh. Either Cartesian or radial coordinates may be selected. Evaluation. SUTRA's evaluation included the three example problems included with the documentation. The model solved the example problems without any difficulty. In addition to the example problems, the model was evaluated against Vauclin's experimental data (Vauclin, Khanji, and Vachaud 1979) and against the saturated analytical solutions of Cases 1, 2, and 3. The model performed satisfactorily. The choice the of coordinate system in SUTRA was useful in solving the test Case 3. Vauclin's experiment. The model was run with the data from Vauclin described in Figures 12-17. The two-dimensional grid was constructed,

88


and the saturation models described in Figures 2 and 3 were used in the simulations. The van Genuchten model had difficulties with the experimental data at low-moisture levels. The pressure (suction) at low-moisture content was very large (negative numbers) and thus created some arithmetic underflow/overflow problems. The Campbell relationship was used with the Vauclin data, and the results are shown in Figure 42. The Campbell model does not predict as large negative pressures as van Genuchten's for those periods of low-moisture content. The results are comparable with those from VS2DT and FEMWATER.

Measured and Calculated Water Table

Positions at Different Times Above Initial Free Surface

0

250 300 100 150 200 Distance (cm) OLD MESH —NEW MESH MEASURED 50

CAMPBELL

L

Figure 42. Water table elevation: Experimental and simulated results

Summary. The model evaluation was satisfactory; SUTRA is recommended for further evaluation. The model was modified to include the four moisture relationships described in Figures 2 and 3. SUTRA's advantages are as follows: the code's maturity (released in 1984 and modified in 1992); the code's versatility (saturated, unsaturated, energy, temperature simulations); and ease of modification.


89

VS2DT

VS2DT is a two-dimensional (vertical cross section, x-z) or axially symmetric three-dimensional (cylinder, r-z) computer code that can be used to solve problems of flow and solute transport in variably saturated porous media. The porous medium may be heterogeneous and anisotropic, but the directions of flow must coincide with the axes of the coordinate system. VS2DT is an extension of the VS2D program, which was developed by USGS to solve flow equations for variably saturated porous media. At present, there is no documentation that describes flow capabilities in VS2DT. Therefore, the user must review VS2D documentation for the aspects of VS2DT. The flow equation used in VS2DT is based on the conservation of mass and Darcy's equation. The flow boundary conditions may be prescribed as known pressure heads, known fluxes, evaporation from surface, plant transpiration, and/or seepage face boundaries. Flow source and/or sink terms such as injection wells or pumping wells also are included in the solution. The flow and mass transport equations were solved numerically using central finite differences about grid-block boundaries. Time derivatives are approximated by ä fully implicit backward finite difference scheme. The effects of advection, dispersion, adsorption, and ion exchange on a chemical can be simulated by VS2DT. The decay of solute mass in the solid phase is also incorporated in the mass transport solution. Both VS2D and VS2DT programs and their documentation are available from the Geraghty and Miller Modeling Group. The available version of VS2DT from Geraghty and Miller is compiled with the Lahey F77L-EM/32 FORTRAN Compiler. A minimum of system requirements for running VS2DT is given as as follows: • 80386 CPU. • 80387 or equivalent math coprocessor. • At least 1 MB of extended memory. • DOS version 3.3 or higher. Equations for flow. The flow equation used in VS2DT (or VS2D) is a combination of a continuity equation and Darcy's flow equation. The equations describe the movement of water under isothermal and isohaline conditions. The governing flow equation is nonlinear and was solved numerically using a block-centered regular finite-difference scheme for spatial discretization and a backward finite difference method for temporal discretization. The nonlinear, discretized flow equation is solved numerically using a modified Newton-Raphson iterative technique. The flow module of VS2DT provides the solution for total hydraulic head. The total hydraulic head is defined as the sum of pressure head and elevation potential. Below the water table, the pressure head is proportional to the weight of the overlying water. Above the water table, water is held in porous media by adsorptive and capillary forces. Therefore, the pressure head in the unsaturated zone is calculated using a capillary pressure formulation. The capillary-rise equation is applied to the movement of water into relatively coarse-grained materials such as silt, sand, and

90


gravel. In media containing a large fraction of clay-size material, adsorption forces may be more significant than capillary forces. The elevation potential is a measure of the gravitational potential resulting from a position relative to an arbitrary datum. In VS2DT, the datum is located at or above the land surface; therefore, the elevation potential is always negative. Initial and boundary conditions. The initial flow conditions in VS2DT can be specified in terms of the initial pressure head or the initial volumetric-moisture content. The program computes the initial condition for the total pressure head from these input parameters. When the moisture content is used for the initial condition, the user must prescribe a relationship between pressure head and moisture content. The water-retention relationship can be coded in a predefined function program of VSTHU or VSTHNV. VSTHU is read in VS2DT and provides volumetric moisture content as a function of pressure head. VSTHNV, also read in VS2DT, defines pressure head as a function of volumetric moisture content. Another type of initial condition is the equilibrium profile, in which the pressure potential is in equilibrium with the elevation potential above the water table. VS2D has an option to automatically compute pressure heads to provide the equilibrium profile. The user can specify a constant minimum pressure head to replace the upper part of the equilibrium profile. For more information, the reader is referred to the VS2DT user's manual. Flow boundary conditions in VS2DT can be specified either as flux, pressure head, or total otentiometric head (pressure head + elevation head). The values of infiltration, evaporation, and discharge through seepage faces also can be specified as boundary conditions. Infiltration and ponding. The effect of infiltration or sprinkler irrigation is coded as a two-stage process. In the first stage, water enters the system at an applied rate until the conductive and sorptive capacity of the medium is exceeded. After the capacities are exceeded, water ponds on the surface, and the infiltration rate decreases asymptotically to a rate equal to the saturated hydraulic conductivity of the medium. VS2DT infiltration options are as follows: a. Specified flux boundary conditions (PFDUM) at the surface equal to the infiltration rate prior to the time ponding occurs, tpond. b. Specified pressure boundary conditions (POND) at the surface equal to the maximum height of ponding after ponding occurs. The ponding time, tpone[, is determined by the model during simulation. Evaporation and evapotranspiration. Evaporation is the amount of soil moisture that escapes from the soil surface due to surface and ambient atmospheric conditions. The evaporation process is formulated as a two-stage process. In the first stage, evaporation occurs when the land surface is wet; thus liquid leaves the system at a rate equal to the atmosphere's evaporation demand. The evaporation rate is referred in VS2DT


91

as potential evaporation rate (PEV). The second stage starts after the source of water to the surface has diminished. The two-stage evaporation process can be expressed by two boundary conditions at land surface: a. Specified surface boundary flux equal to the potential evaporation demand, until there is not enough water to meet this demand. b. Specified surface boundary flux as function of the pressure potential gradient between the soil and the atmosphere. VS2DT handles boundary condition transition for the two-stage process. Potential evaporation in VS2DT is implemented using an empirical formulation. The value is changed with time in a user-defined manner. Details of numerical implementation are given in the VS2DT user's manual. Transpiration is the amount of soil moisture that can be removed by plant-root extraction. Transpiration is treated in VS2DT as a sink term. The rate of water withdrawal is formulated using an empirical equation. To simulate a problem with evapotranspiration, the logical variable (ETSIM) in the input file must be set to TRUE. In addition, values for the variables, PET (potential transpiration), HROOT (minimum pressure in roots), RTDPTH (the depth of rooting), RTBOT (the root activity at the bottom of the root zone), and RTTOP (the root activity at land surface) must be specified. Refer to the VS2DT user's manual for further information. Seepage faces and sink terms. Seepage faces are boundaries where a phreatic surface of a flow domain terminates on a land surface. At a seepage face boundary, the total pressure head is equal to the potential elevation head. Examples of seepage faces are boundaries along stream banks, spring discharge zones, and well bores that tap unconfined aquifers. The upper limit of a seepage face is determined by the location of the water table, which is unknown. The location of this intersection is part of the solution. Therefore, determining the seepage face boundaries is a nonlinear problem. VS2DT solves seepage face problems iteratively. Flow source and sink terms can be specified in VS2DT. Source terms include injection wells {l?IT) and drip-irrigation {LIT) devices; sink terms include pumping wells (L?/T) and suction lysimeters {LIT). Evapotranspiration or plant-root extraction can also be treated in VS2DT as sink terms. Equations for solute transport. The formulation used for solute transport modules in VS2DT includes an advection term, a hydrodynamic dispersion (mechanical + molecular) term, and source/sink terms. Source/ sink terms include a fluid source/or sink, adsorption, decay, and ionexchange reactions in solution. The decay of a solute (such as radioactive decay) is incorporated by a linear relationship between the sink term and the concentration of solute. The solute adsorption from the water phase onto the solid phase is given in a special case of the Freundlich isotherm (n = 1) as a constant ratio between the solid phase and water (liquid) phase, linear partition. For nonionic organic chemicals, this ratio, K, represents adsorption onto organic 92


matter in soils. Nonlinear adsorption between the solid and liquid phases is given by the Langmuir and Freundlich isotherms. Ion exchange is another type of reaction that has been included in VS2DT. Four types of ion exchange are coded in VS2DT: monovalent-monovalent exchange (such as the exchange of sodium and potassium), divalent-divalent exchange (such as the exchange of calcium and strontium), monovalent-divalent exchange (such as the exchange of sodium with calcium), and divalentmonovalent exchange (such as the exchange of calcium with sodium). Detailed information on adsorption and ion exchange can be found in books such as Feeter (1993). Initial and boundary conditions. Initial conditions for solute concentration can be specified either as a fixed constant concentration in the main input file or read from a user-defined file (unit IU). Two types of solute boundary conditions can be specified in VS2DT, constant concentration and mass flux condition. In addition, if a fluid source exists, the concentration entering the system must be specified. The evaporation boundary condition is treated in a unique form, different from other boundary conditions. Evaporating water is assumed free of chemical contamination. Sources and sinks. Six source/sink options are available in VS2DT: Freundlich isotherm, Langmuir isotherm, and four ion-exchange options defined previously. Linear adsorption can be modeled using the Freundlich isotherm with the exponent set 1. The present version of VS2DT is set up to use the Langmuir isotherm. The other five options are not active. To activate each option, the user needs to remove comment (Q parameters in front of the selected option in the function subprogram, VTRET, and recompile and load the programs. In addition, proper flag and input parameters must be specified in the input file. Only one option can be used per simulation. In other words, for each option simulation, VTRET must be changed; the programs need to be compiled and linked. Variable adsorption rate and ion exchange for different texture classes of soil are possible by varying the coefficients. Input/output parameters. Data for VS2DT simulation are read from a user-created ASCII (text) input file. The numerical values of parameters are read as free-formatted input. Entry of data using the form n*d results in n values of d being read into the program. Each event (e.g., infiltration event) must be ended by 999999 /; the end of the input record is also invoked by 999999 /. A successful simulation of VS2DT requires the definition of input parameters and flags in proper order. An easy way to create an input file is to modify an existing input file by adding or removing parameters required for the specific problem. VS2DT creates a main output file and other files that store individual output parameters as requested in the input file. The output file names are assigned by the user. Evaluation. Example data sets included with the model ran without difficulties. In addition, two problems were selected for further testing. Chapter 4 Models Description

93

Vauclin's experiment defined in the test cases section was used in the evaluation of the variable saturation formulations of VS2DT. A second test case, an injection well into a radial flow domain, was selected to evaluate both the saturated formulations and the radial coordinate system. Variably saturated flow using tabulated initial pressure condition. In this example, VS2DT is used to simulate flow in a variably saturated soil system reported by Vauclin, Khanji, and Vachaud (1979). The domain is a soil slab 3 m long and 2 m high and 5 cm thick (Figure 10). The soil was packed as homogeneously as possible with average bulk density of 1.57 g/cm3. At one end of the slab, a constant head reservoir was located. The water table was imposed at 135 cm (depth). A constant flux at the surface, q = 14.8 cm/hr, was applied over a width of 50 cm. The saturated hydraulic conductivity of the fine sand was 35 cm/hr. Tabulated initial pressure heads were used in this simulation (Figure 12). Simulation results and comparison against experimental data are shown in Figures 43 and 44.

0 00 "1

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X (cm) Figure 43.

Water table simulation

Injecting a conservative tracer in a radial flow system. In this example, fluid is injected into a fully saturated confined aquifer. Initially, the solute concentration in the aquifer is 0. The injected water has the concentration of 1. A variable spacing in vertical and horizontal directions were used. The hydraulic conductivity, the longitudinal, and the transverse dispersivity are set to K = 0.36 m/hr, aL = 10.0 m, and aT = 0.0 m. A pumping period of 2,200 hr was simulated. Flow boundaries consisted of a constant flux of 225 m3/hr at the injection well and a fixed head of 10.0 m at the radial boundary. VS2DT results are shown in Figure 45. Model simulation and analytic solution fall on top of each other.

94


VS2DT(2hr) Vauclin VS2DT(4hr) Vauclin VS2DT(8hr) Vauclin

300

Figure 44.

Simulated water table versus experimental data (Vauclin, Khanji, and Vachaud 1979)

Verification Problem Effect of Recharge Weil 1.0 0.9 0.8

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Figure 45.


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Figure 54.

PCE liquid phase saturations after release of 4 days of redistribution in a homogeneous medium (K1 = K2 = K3)

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Figure 55.

PCE liquid phase saturations after release of 2 days of redistribution in a mildly heterogeneous medium (K3 > K1 > K2)


109

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DNAPL saturation after 4 days of redistribution in „ § mildly heterogeneous medit ' (K3>K1>K2).

Elevation Z(m),

Initial Water Table

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Figure 56.

PCE liquid phase saturations after release of 4 days of redistribution in a mildly heterogeneous medium (K3 > K1 > K2)

of media heterogeneities relegate the current generation of codes to idealized process design. Limited technical support for MOFAT is available from CSMOS. Environmental Systems and Technologies, Inc., developed MOFAT for the EPA and provides support for both MOFAT and MOTRANS. Some of the limitations that impede the application of MOFAT, as well as other MPFT codes, to complex field simulations include the following: • The MOFAT is a relatively new code (released in 1992) and therefore has a minimal track record for field applications. Likewise, MOTRANS (circa 1991) has had limited field application. • Parameters for MPFT codes may be difficult to obtain, particularly the constitutive relation parameters. However, MOFAT is not unique in this regard. Any MPFT model likely would have the same problem. Some specific limitations of MOFAT include the following: • The assumption of noninteracting constituents in MOFAT, i.e., the partitioning of one does not affect the partitioning of another, is an acceptable assumption for mixtures of nonpolar, saturated hydrocarbons that are sparingly soluble in water. However, this assumption would fail for systems involving contaminants with polar functional groups (e.g., nitroaromatics, alcohols, phenols).

110


The weak coupling between flow and transport assumed in MOFAT precludes application to remediation simulations involving strongly coupled processes, such as cosolvent flushing. Restriction to linear rectangular elements simplifies tessellation and supports use of the influence coefficient method, but defeats one of the major, potential advantages of the finite element method—the flexibility in adjusting the grid design to accommodate special features (wells, interfaces, etc.) or fitting irregular boundaries so common in the subsurface. Users cannot readily assign oil saturations as initial conditions, which one might want to do if residual saturation is assumed or saturations are known. One can assign the appropriate oil phase pressure based on the constitutive model. Several code features are not fully explained in the documentation; for example, the adaptive solution domain approach is described but never used in an example problem.


5

Model Evaluation Summary

MOC MOC recommendations are based on both the evaluation results and the literature. Overall MOC performed satisfactory when evaluated. Figure 57 shows MOC developers and features. MOC evaluation highlights are as follows: • USGS-MOC is a popular and well-established code that is well suited to the design of simple containment or remediation schemes (e.g., a screening model or pump-and-treat). • The method of characteristics remains a useful tool for the simulation of advection-dominated transport. • Lack of flexibility in discretization and boundary conditions limits the general applicability of USGS-MOC for remediation design. Other MOC-based transport codes offer greater flexibility and further development (e.g., MT3D with MODFLOW). USGS-MOC is a mature code in that it is well documented and relatively "bug" free. Any problems are likely due to intrinsic limitations of the numerical methods or model design. The code can be obtained free of charge from the USGS through either bulletin boards or the Internet. If a hard copy manual is desired, then the code may be obtained from WATSTORE for a nominal charge. Due to its longevity and ease of use, the code is available through numerous vendors, including the following: • U.S. Geological Survey WATSTORE; Reston, VA. • Geraghty and Miller, Modeling Group; Reston, VA. • International Groundwater Modeling Center, Golden, CO. • Scientific Software Group, Washington, DC.

112

Chapter 5 Model Evaluation Summary

USGS - MOC (USGS - 2-D - TRANSPORT) Version

3.0(11/89); MOC386

Vendor (for the version tested herein)

Geraghty and Miller, Inc. 10700 Parkridge Boulevard, Suite 600 Reston, VA 22091 (703)758-1200

Cost

$300 includes a utility to convert output files to SURFER grid files and extended memory version of the code. Cost varies among the vendors.

Developers

L. F. Konikow and J. D. Bredehoeft (1978) D. J. Goode and L F. Konikow (1989) U.S. Geological Survey-Water Resources Division Reston, VA

Source Code

FORTRAN IV Public domain; available as document and ASCII file

Documentation

Adequate; USGS documents

Input/Output

User-designated input and output ASCII files Originally formatted input; input to support subsequent modifications are unformatted

Platform

PC to mainframe, depending on scale and complexity of the problem. The MOC3"6 version requires a 386 CPU, a math coprocessor, at least 1 MB of extended memory, and DOS 3.x.

Platform Evaluated

Evaluated on 486/33MHZ machine with 8 MB RAM.

GMS Status

Not in the GMS

Figure 57.

MOC highlights

MODFLOW Figure 58 shows a summary of MODFLOW features. Because the MODFLOW model is very popular and is in the public domain, many vendors add some additional capabilities to the model and resell it. The USGS still distributes the code in its basic form. Figure 59 lists some (not all) of the vendors that sell the MODFLOW program. MODFLOW is recommended for groundwater flow problems that do not involve temperature variation, density variation (e.g., salt water and fresh water), unsaturated flow, or nonaqueous-phase contaminants. It is not applicable for fractures or heterogeneous porous media that cannot be reasonably represented by many, small rectangles. For transport problems, MODFLOW can be used with a transport model such as MODPATH for advection only. Pathline codes, like MODPATH and GWPATH, that track the advective movement of a conservative tracer in the absence of dispersion are useful for preliminary analyses of Chapter 5 Model Evaluation Summary

113

,

,

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MODFLOW: A Modular Three-Dimensional Finite-Difference Groundwater Flow Model Version

MODFLOW PC/EXT v. 1.31 (3/93)


International Ground Water Modeling Center (IGWMC) Colorado School of Mines Golden, CO 80401-1887 (303)273-3103

Cost

$350 includes PREMOD, POSTMOD, and extended and virtual memory versions of the code. Cost varies among vendors. See the table of vendors later in this document.

Developers

Michael G. McDonald and Arlen W. Harbaugh (1984,1988) U.S. Geological Survey, Reston, VA.

Source Code

Written in FORTRAN 66, minimally upgraded to FORTRAN 77. Code is in the public domain; source code is distributed.

Documentation

Adequate; USGS Reports

Input/Output

input is from several ASCII files. Output consists of both formatted and unformatted files.

Platform

Designed to be portable and has been run on a variety of computer platforms. The executable program provided was compiled with Lahey's F77L-EM/32 v. 5.0 extended memory FORTRAN compiler. Execution requires an 80386/80486 processor with a math coprocessor, at least 2 MB of RAM, and at least 3 MB of hard disk space (more is recommended). With less than 4 MB of RAM, the virtual memory version of the model must be run, which is much slower.

Platform Evaluated

These evaluations were performed on an 80486/50MHz computer with 8 MB RAM.

GM Status

In the GMS

Figure 58.

MODFLOW highlights

minimum travel times, contaminant origination, and for chasing problems in flow solutions. However, for quantitative evaluation of contaminant concentrations, a model like MT3D is needed. The MT3D program provides a much more realistic and detailed picture of transport than do advection-only pathline programs. The MT3D-compatible version of the model, MODFLOW/mt is probably a wise choice for use with MT3D because the linkages between the codes have already been performed. Because of MODFLOW's popularity, many additional software routines and products are available to improve the usability or extend the capabilities of the MODFLOW program. Some were written by the USGS and others by private companies. Table 8, although quite long, is an incomplete list of the many products available.

114


Some Vendors of the MODFLOW Program Model Name

Distributor

Cost

Includes

MODFLOW

USGS

$40

Support by the USGS.

MODFLOW PC-EXT

International Ground Water Modeling Center

$350

Extended and virtual memory versions with PREMOD and POSTMOD.

MODFLOWEM

Scientific Software Group

$339

Extended memory version includes ZONEBUDGET and technical support from McDonaldMorrisey Associates.

MODFLOW386

Geraghty and Miller

$300

Extended memory version with utilities and support.

MODFLOWMAC

Geraghty and Miller

$375

Macintosh version of the MODFLOW program. Includes support.

MODFLOW/mt

S. S. Papadopulos and Associates, Inc.

Included wrth MT3D

Extended memory version with utilities. Writes the unformatted file containing data required by MT3D.

MODFLOWP

USGS

$40

Basic program plus parameter estimation capability.

Figure 59.

MODFLOW vendors (Not a complete listing but is intended to provide an example. Inclusion herein does not indicate sanction by the U.S. Government, etc.)

Table 8 Support Software for MODFLOW Program Title

Developer (if known)

Distributor (addresses below)

Cost

Brief Description

RADMOD

Riley and Harbaugh

USGS

$40

Computes cylindrical flow to a well.

MODMAN

Greenwald

GeoTrans, Inc.

$1,500

Optimization of pumping rates in MODFLOW.

ZONEBUDGET

Harbaugh

USGS

$40

Calculates subregional water budgets such as flow to/from a river, etc.

MODINP

TECSOFT, Inc.


$150

Preprocessor for MODFLOW input files.

MODELCAD386

Rumbaugh

Geraghty and Miller

$750

Graphical preprocessor for MODFLOW, MOC, MT3D, and MODPATH.

MMSP

Scott

USGS

$40

Statistical processor for analyzing MODFLOW output.

PM

Chiang and Kinzelbach


$350

Graphical preprocessor and postprocessor for MODFLOW and MODPATH. (Continued)


115

Table 8. (Concluded) Program Title

Developer (if known)

MODFLOW386 Utilities

Distributor (addresses below)

Cost

Brief Description

Geraghty and Miller

$100

Includes conversion programs for unformatted to ASCII, and for SURFER graphics, also calibration statistics, etc

MODPATH

David Pollack

USGS

$40

Particle tracking for steady-state, advection-only transport.

MODPATHEM

David Pollack


$350

Extended memory version of the USGS model. Supported.

MODPATH-

David Pollack

USGS

$350

Display/analysis of MODPATH results. Supported.

MODGRAFEM


$425

Creates velocity vectors and head contour plots from MODFLOW output.

MODINVEM


$800

Modeling tool kit including MODFLOW, parameter estimation, and preprocessor and postprocessors.

MODVELEM


$150

Creates an unformatted velocity file for use by MODGRAF.

MODCELLEM


$150

Converts unformatted cell-by-cell flow terms to ASCII files for viewing/printing.

MODLOCALEM


$995

Constructs local MODFLOW input files from regional MODFLOW files.

MODRET


$325

Couples MODFLOW with an infiltration program to simulate storm water retention ponds.


$150

Preprocessor for MODPATH.

Golden Software, Inc.

$499

Graphics program for displaying contours and surface maps.

PLOTEM

MPATHINEM

TECSOFT, Inc.

SURFER

MT3D For a saturated medium in which the flow and transport solutions can be decoupled, the use of MODFLOW/mt with MT3D is recommended. The models are sufficiently simple that set up, and modification can be performed in a reasonable time frame. However, when combined, these models have most capabilities required for routine saturated-zone flow and transport modeling. Although users new to MT3D and MODFLOW likely will be overwhelmed with the abundance of input possibilities and choices for output formats and locations, those already familiar with MODFLOW will be immediately comfortable with MT3D's structured, uncommented style of ASCII input files. The program was constructed to be an add-on to MODFLOW, although it will accept head information from other sources. 116


There are many advantages to this linkage. The MODFLOW package is very dynamic with a large user community that is developing additional modules or packages to solve previously unresolved problems. Overall, if the user can live with some of the mass balance "errors" that the MOC solution inherently carries, and the limitations of MODFLOW as discussed previously, then the MODFLOW/mt with MT3D package is recommended. Figure 60 shows MT3D features. MODFLOW is already included in the Groundwater Modeling System (GMS), the WES-developed comprehensive graphical environment for numerical modeling. The GMS provides tools for site characterization, model conceptualization, mesh and grid generation, geostatistics, and postprocessing. MT3D was included in the GMS by the end of FY95. MT3D: A Modular Three-Dimensional Transport Model Version

1.8(10/92)

Vendor/Distributor

S. S. Papadopulos and Associates, Inc. (SSP&A) 7944 Wisconsin Avenue Bethesda, M D 20814 (301) 718-8900 Center for Subsurface Modeling Support (CSMoS) (Version 1.2 only) Robert S. Kerr Environmental Research Laboratory USEPA P.O. Box 1198 Ada, OK 74820 (405)436-8500

Cost

$450 including MT3D source code and executable, utility programs, and MODFLOW/mt (SSP&A's MODFLOW)

Developer

Chunmiao Zheng (1990, 1992,1993), formerly at SSP&A, now at the University of Alabama

Source Code

FORTRAN 77 (except the IMPLICIT NONE statement). The executable provided contains FORTRAN 90 dynamic memory allocation. Proprietary program but source code is distributed.

Documentation

Very Good

Input/Output

Input from the flow solution is unformatted. Most other input and output files are ASCII files.

Platform

PC to mainframe, depending on complexity of problem. The executable program provided was compiled with Lahey's F77L-EM/32 v. 5.01 extended memory FORTRAN compiler. Execution requires an 80386/80486 processor with math coprocessor, at least 2 MB of RAM and at least 1 MB of hard disk space (more is recommended).

Platform Evaluated These evaluations were performed on an 80486/50MHZ computer with 8 MB RAM GMS Status

Figure 60.

Was included in the GMS by late FY95

MT3D highlights


117

PLASM PLASM is an excellent teaching tool, has significant support, and is recommended as a screening model. PLASM runs on many platforms, is efficient, and has significant third-party support. PLASM needs a graphical interface to facilitate its use as a screening model. Figure 61 presents a summary of PLASM's features. PLASM Version

2.0 (8/90); IGWMC # FOS12

Vendor/Distributor

International Ground Water Modeling Center (IGWMC) Colorado School of Mines Golden, CO 80401-1887 (303) 273-3103

Cost

$120 includes a package of three finite-difference programs and a preprocessor.

Developer

T. A. Prickett and C. G. Lonquist Illinois State Water Survey Champaign, IL 1971

Language

FORTRAN 77.

Code

Complete source code, documentation, example input data sets, and executables (CONPLASM, UNCPLASM, and PREPLASM) provided on floppy disks.

Documentation

Documentation includes that describing the modifications by Paul van Der Heijde and the original Illinois State Water Survey Bulletin 55.

Input

Input data files were created using the preprocessor PREPLASM. Once the input data file is created with PREPLASM, then the file is copied into either conplasm.i05 or uncplasm.i05 file and the PLASM program is executed.

Output

Output files created by PLASM (CONPLASM or UNCPLASM) are plasm.o06 and plasm.o08. The file plasm.o06 is an echo of the input data; the file plasm.o08 is the head distribution for the simulation.

Platform

PC to mainframe, depending on the scale and complexity of the problem. The IGWMC version is compiled with Microsoft FORTRAN Version 4.1, and the preprocessor was compiled with QuickBasic 4.0. Minimum hardware requirements are a PC-compatible 8086/80286/80386/80486 based system with 640 K RAM and DOS 2.0 or higher.

Platform Evaluated

Evaluated on a 486/66MHz PC with 32 MB of RAM.

GMS Status

Not in the GMS

Figure 61. PLASM'S features

118


RANDOM WALK RANDOM WALK and RAND3D are the two- and three-dimensional groundwater models for solute transport based on the RANDOM-WALK algorithm. Both models have a significant number of users in private consulting and in the Army. RAND3D is fairly easy to use once a user becomes familiar with the code. A graphical user interface will significantly benefit both models, since input file generation is painful. Most of the concerns associated with RAND3D should be resolved with its new release. Figures 62 and 63 summarize both RANDOM WALK and RAND3D, respectively. RANDOM WALK Version

1.0;IGWMCFOS#13

Vendor/Distributor

International Ground Water Modeling Center (IGWMC) Colorado School of Mines Golden, CO 80401-1887 (303) 273-3103

Cost

$100 includes FORTRAN source, executable, and three example data sets for the IGWMC RANDOM WALK.

Developer

T. A. Prickett, T. G. Naymik, and C. G. Lonnquist Illinois State Water Survey Champaign, IL 1981

Language

FORTRAN 77.

Code

Complete source code, executable, and three example data sets provided on floppy disk.

Documentation

Complete, includes two Illinois State Water Survey reports: Bulletins 55 and 65.

Input

Example problems available on floppy disk.

Output

Output files that can be displayed on SURFER.

Platform

486 PC to mainframe, the version evaluated was for the PCcompatible environment: 80286/80386/80486. Minimum requirements are 640 KB of RAM and a minimum of 1 MB of disk space, although more is recommended.

Platform Evaluated Evaluated on a 486/25MHz PC with MB of RAM. GMS Status

Figure 62.

Not in the GMS

RANDOM WALK highlights


119

RANDOM WALK-3D Version

RAND3D

Vendor/Distributor

RANDOM WALK-3D Donald Koch Engineering Technologies Associates 3458 Ellicott Center Drive Ellicott City, MD 21043 (301)461-9920

Cost

No charge, includes basic source code, executable, an example data set, and PREMOD3D (a preprocessor that creates input files for RAND3D from MODFLOW output.

Developer

Donald Koch (Same as distributor)

Language

Microsoft Quick Basic

Code

Basic source code provided on a floppy disk; the preprocessor PREMOD3D is written in FORTRAN. Code is interactive.

Documentation

Available.

Input

Data file (head) from a groundwater flow model like MODFLOW. Example problem is included with the model on floppy disk.

Output

Results are displayed graphically.

Platform

PC only. Execution requires an 80286/80386/80486 processor with math coprocessor, at least 640 KB of RAM, and at least 1 MB of hard disk space (more is highly recommended).

Platform Evaluated

Evaluated on a 486MHz PC.

GMS Status

Will be included in the GMS in late FY97 or early FY98.

Figure 63. RAND3D highlights

120


FEMWATER and LEWASTE The models did an acceptable job of simulating the unsaturated/ saturated flow in porous media tested. The models have a significant number of choices and options; with the aid of a graphical user interface, FEMWATER/LEWASTE should be considered for many subsurface problems. Figures 64 and 65 describe the most important features, vendors, and developer of both models. Both models are now part of the GMS. FEMWATER Version

3-D EPA.

Vendor/Distributor

Same as developer, Dr. George Yeh

Cost

N/C

Developer

G. T. (George) Yeh Department of Civil Engineering Pennsylvania State University University Park, PA 16802

Language

FORTRAN 77.

Code

Complete source code provided in an ASCII file on floppy disk.

Documentation


Input

Data file partly in fixed and partly in free-field format. Example problems available on floppy disk.

Output


Memory Requirements

Vary depending on size of problem. Easily adjustable by changing PARAMETER statements in .inc files.

Platform


Platform Evaluated

Silicon Graphics workstation

GMS Status

In the GMS

Figure 64.

FEMWATER characteristics


121

LEWASTE Verston

3-D EPA.

Vendor/Distributor

Same as developer, Dr. George Yeh

Cost

No charge

Developer

G. T. (George) Yeh Department of Civil Engineering Pennsylvania State University University Park, PA 16802

Language

FORTRAN 77.

Code

Complete source code provided in an ASCII file on floppy disk.

Documentation


Input

Data file partly in fixed and partly in free-field format. Example problems available on floppy disk.

Output


Memory Requirements

Vary depending on size of problem. Easily adjustable by changing PARAMETER statements in .inc files.

Platform


Platform Evaluated

Silicon Graphics workstation.

GMS Status

In the GMS.

Figure 65.

122

LEWASTE characteristics


UNSAT1 UNSATl simulates flow in the unsaturated or vadose zone. The model's performance was similar to that of CHEMFLO; thus it is recommended that a program like CHEMFLO or PRZM-2 be included for further evaluation rather than UNSATl. Both CHEMFLO and PRZM-2 include solute transport which UNSATl lacks. Figure 66 summarizes UNSATl. UNSAT1: A One-Dimensional Finite Element Model for Unsaturated Flow Version

1.0;IGWMC-FOS18PC


International Ground Water Modeling Center (IGWMC) Colorado School of Mines Golden, CO 80401-1887 (303)273-3103

Cost

$50 includes PREMOD, POSTMOD, and extended and virtual memory versions of the code. Cost varies among vendors. See the table of vendors later in this document.

Developers

M. Th. van Genuchten Princeton University, Princeton, NJ

Source Code

Written in ANSI FORTRAN. Code is in the public domain, source code is distributed.

Documentation

Adequate, USGS Reports

Input/Output

Input is from several ASCII files. Output consists of both formatted and unformatted files.

Platform

Variations/modifications of UNSAT1 may be run on different platforms. The executable program provided was compiled with Microsoft's FORTRAN Version 3.2 compiler. Execution requires an IBM-PC, XT, AT, 80386/80486 processor with a math coprocessor, at least 512 K of RAM, and DOS 2.0 or above.

Platform Evaluated


GMS Status

Not in the GMS

Figure 66.

UNSAT1 highlights


123

CHEMFLO CHEMFLO performed satisfactorily in the unsaturated zone evaluation. The software is a good screening tool and an excellent teaching tool. The model/software is recommended for simple unsaturated zone flow and transport modeling. In addition, it is highly recommended as a "first cut" approach, especially for unsaturated zone problems lacking soil and chemical data. CHEMFLO compares favorably with UNSAT1, another one-dimensional unsaturated flow model, in simulating Prill, Johnson, and Morris's (1965) column drainage experiment. One advantage that CHEMFLO has over UNSAT1 is its "user friendly" interface. Figure 67 highlights CHEMFLO's features. CHEMFLO: A One-Dimensional Water and Chemical Transport Model Version

1.3

Vendor/Distributor

Center for Subsurface Modeling Support (CSMoS) Robert S. Kerr Environmental Research Laboratory USEPA P.O. Box 1198 Ada, OK 74820 (405) 436-8500

Cost

No charge for executable and example case.

Developer

D. L. Nofziger, K. Rajender, Sivaram K. Nayudu, and Pei-Yao Su (1989) Department of Agronomy Oklahoma State University Stillwater, OK

Source Code

None

Documentation

Good; EPA manual.

Input/Output

Interactive input. There is a soils properties database file included with the executable. Output files are ASCII files.

Platform

PC only. Execution requires an 80286/80386/80486 processor with math coprocessor, at least 640 KB of RAM, and at least 1 MB of hard disk space (more is highly recommended).

Platform Evaluated


GMS Status

Not in the GMS

Figure 67.

124

CHEMFLO characteristics


PRZM-2 PRZM-2 is a collection of models to predict pesticide fate and transport in agricultural soils. The tool consists of two modules: PRZM, a pesticide root zone model, and VADOFT, a vadose zone model. The model has an extensive chemical database, has guidance on parameter selection for different areas of the country, and incorporates meteorological inputs. The model needs an interactive or graphical user interface. PRZM-2 would benefit significantly from a modeling system such as the GMS. Model evaluation up to this point consisted of examples included with the documentation. PRZM-2 will be evaluated with chemical field data in the near future. The model is highly recommended for sites where crops or plant growth is significant. Figure 68 shows PRZM-2's features. PRZM-2: Pesticide Fate in the Crop Root and Unsaturated Soil Zones Version

1.02

Vendor/Distributor (for the version tested herein)

Center for Exposure Assessment Modeling (CEAM) Environmental Research Laboratory U.S. Environmental Protection Agency 960 College Station Road Athens, GA 30606-2720 (706) 546-3549

Cost

No charge; includes WordPerfect documentation and an extended memory version of the code.

Developers

J. A. Mullins, R. F. Carsel, J. E. Scarbrough, and A. M. Ivery (1993) AScI Corporation Athens, GA U.S. Environmental Protection Agency Athens, GA

Source Code

FORTRAN-77 Public domain; available as document and ASCII file

Documentation

Good; EPA manual

Input/Output

Several input files are needed for a PRZM2 run; as a minimum a meteorological file (MET.INP), a command file (PRZM2.RUN), and at least one of the modules files: PRZM.INP, VADOFT.INP, and/or MC.INP Output files consist of the run output file PRZM.OUT and the time series (TIMES.OUT and VADF.OUT) files from the PRZM module and the vadose module.

Platform

PC, PRIME 50 minicomputer, SUN SPARC under UNIX/SUNOS,and DEC VAX systems. The executable program provided was compiled with Lahey's F77-EM/32 version 5.01. Execution requires a 386 or 486 CPU, a math coprocessor, 640 K base memory, at least 4 MB of extended memory, at least 4.5 MB of hard disk space and DOS 3.x or higher.

Platform Evaluated

Evaluated on 486/66MHz machine with 8 MB RAM.

GMS Status

Not in the GMS

Figure 68.

PRZM-2 overview


125

SUTRA SUTRA performed favorably in overall evaluation, including the example evaluation, the test cases, and Vauclin's experiment. The model is very versatile and powerful, has a significant user group, and shows promise for future development. Figure 69 shows its highlights. SUTRA is available through numerous vendors, including the following: • U.S. Geological Survey WATSTORE; Reston, VA. • Geraghty and Miller, Modeling Group; Reston, VA. • International Groundwater Modeling Center, Golden, CO. • Scientific Software Group, Washington, DC. SUTRA: Saturated-Unsaturated TRAnsport Version

SUTRA386 Version 1.0


Geraghty and Miller, Inc. 10700 Parkridge Boulevard, Suite 600 Reston, VA 22091 (703)758-1200

Cost

$300 includes postprocessing utility to convert output files to SURFER grid files and extended and virtual memory versions of the code. Cost varies among vendors. See the table of vendors later in this document.

Developers

Clifford I. Voss (1984) WRIR 84-4369 U.S. Geological Survey, Reston, VA.

Source Code

Written in standard ANSI FORTRAN. Code is in the public domain.

Documentation

Adequate-good, USGS Reports

Input/Output

Input is from two ASCII files. One with all of the data necessary for simulation, the other with initial conditions of pressure and concentration or temperature. Output consists of one or two files. One contains the output of the simulation; the second is optional and contains output at a time step similar to the initial conditions. The second output file is used for restart.

Platform

The executable program provided was compiled with Lahey's F77LEM/32 FORTRAN compiler and the OS/386 software developed by Ergo Computing, Inc. Execution requires an 80386/80486 processor with a math coprocessor, at least 1 MB of RAM. The executables included in the version evaluated required 1 MB, 3 MB, or 7 MB of RAM.

Platform Evaluated


GMS Status

Not in the GMS

Figure 69.

126

SUTRA highlights


VS2DT VS2DT performed favorably for problems provided in its user's manual. In addition, the program was examined against a published laboratory experiment and numerical solution. Results of VS2DT simulations were in good agreement with the published data. The example problems involved physical processes such as infiltration, evaporation, evapotranspiration, and injection wells in radial flow. The soil conditions in these examples ranged from fully saturated, to fully unsaturated, to mixed unsaturated-saturated zone conditions. The fluid density in VS2DT is fixed to be 1.0 g/cm3. Hence, all other parameters must be input in units of grams and centimeters; time can be in seconds, minutes, hours, etc. VS2DT required small time steps and fine spatial discretization to achieve convergence and obtain a stable solution for the unsaturated-saturated example problem (Vauclin's Experiment). VS2DT has four options to specify the water-retention relationship between pressure head and water content. These options are a user-defined or measured value, the BrooksCorey equation, the Haverkamp equation, and the van Genuchten formulation. All options were tested using the default parameters coded in VS2DT. The user-defined or tabulated option for pressure head-water content did not work properly. Overall, VS2DT shows promise as a saturated and couple unsaturated/ saturated groundwater code. The code needs some modifications to make it more general and easier to use; there should be no need to recompile the code to select different options. The code would benefit from the GMS interface. Figure 70 shows VS2DT's characteristics, developer, and other relevant information. Refer to the list of vendors in the previous section for VS2DT resellers.


127

...

_

VS2DT: Solute Transport in Variably Saturated Porous Media 0 Version I Vendor (for the ver1 sion tested herein)

VS2DT386 Version 1.0 Geraghty and Miller, Inc. 10700 Parkridge Boulevard, Suite 600 Reston, VA 22091 (703)758-1200

Cost

$300 includes postprocessing utility, extended and virtual memory versions of the code. Cost varies among vendors. See the table of vendors later in this document

Developers

R. W. Healy (1990) WRIR 90-4025 (Transport) E. G. Lappala, R. W. Healy, and E. P. Weeks (1987) WRIR 83-4099 (Flow) U.S. Geological Survey, Reston, VA.

Source Code

Written in standard ANSI FORTRAN. Code is in the public domain.

Documentation

Adequate, USGS Reports

input/Output

Input is from several ASCII files. Output consists of both formatted and unformatted files.

Platform

The executable program provided was compiled with Lahey's F77LEM/32 FORTRAN compiler and the OS/386 software developed by Ergo Computing, Inc. Execution requires an 80386/80486 processor with a math coprocessor, at least 1 MB of RAM.

Platform Evaluated


GMS Status

Not in the GMS

Figure 70. VS2DT characteristics

128


MOFAT and MOTRANS MOFAT results matched the documentation simulations well. The current state of the art in multiphase flow and transport (MPFT) modeling is still inadequate. Regardless of the relative sophistication of MOFAT, all such models are of unknown utility in field-scale application. Difficulties in site-specific parameter identification and uncertainties regarding subsurface processes and the influence of media heterogeneities relegate the current generation of codes to idealized process design. MOFAT is presently the only readily available multiphase flow and transport code in the public domain. Other codes are either for multiphase flow only or assume residual NAPL saturation. Figure 71 shows MOFAT's features and distribution sources. MOFAT's limitations as a remediation model are those expected of a fairly new and complex model. In particular, the code has a minimal track record for field applications; parameters for MPFT codes may be difficult to obtain, particularly the constitutive relation parameters; and MOFAT treats NAPL constituents as noninteracting, i.e., the partitioning of one does not affect the partitioning of another. On the other hand, MOFAT is capable of simulating NAPL release, dispersal, and partitioning into aqueous and vapor phases. Predictions of free (mobile) and residual NAPL distribution are possible. The code is recommended for pump-and-treat and vapor extraction recovery systems where NAPL are present. Figure 72 presents a list of groundwater software vendors.


129

MOFAT Version

1.0(1991)

Source/Vendor

Center for Subsurface Modeling Support (CSMoS) R. S. Kerr Environmental Research Laboratory (RSKERL) U.S. EPA - Office of Research and Development Ada, OK 74820 (405) 332-8800 (x245)

Developers

Kaluarachchi and Parker (1989, 1990) Katyal, Kaluarachchi, and Parker (1991) Center for Environmental and Hazardous Material Studies Virginia Polytechnic Institute and State University Blacksburg, VA 24061-0404

Source Code

FORTRAN 77 MOFAT: public domain, available as ASCII file from CSMoS MOTRANS: proprietary version; executables only from ES&T

Documentation

Document prepared for EPA-RSKERL

input /Output

Formatted ASCII input files; PREMOF: menu-driven, preprocessor with MOFAT. Output files are formatted ASCII; user has some control over frequency of output

Platform

Dependent on scale and complexity of the simulation. MOFAT optimally requires 10 MB RAM on a 386-CPU with math coprocessor (or 486). MOFATVM is a virtual memory version with more reasonable RAM requirements, though at a speed cost.

Platform Evaluated

MOFATVM was evaluated on 486/33MHz machine with 8 MB RAM.

GMS Status

Not in the GMS

Figure 71.

MOFAT highlights

Vendors' Addresses USGS Water Resources Division 437 National Center 12201 Sunrise Valley Drive Reston, VA 22092 (703) 648-5695

Scientific Software Group P.O. Box 23041 Washington, DC (703) 620-9214

Geraghty and Miller, Inc. Modeling Group 10700 Parkridge Boulevard Suite 600 Reston, VA 22091 (703) 758-1200

S. S. Papadopulos and Associates, Inc. 7944 Wisconsin Avenue Bethesda, MD 20814 (301) 718-8900

Golden Software, Inc. 809 14th Street Golden, CO 80402-0281 (303) 279-1021

International Ground Water Modeling Center Colorado School of Mines Golden, CO 80401-1887 (303) 273-3103

GeoTrans, Inc. 46050 Manekin Plaza Suite 100 Sterling, VA 20166 (703) 444-7000

Figure 72. 130

General groundwater software vendors Chapter 5 Model Evaluation Summary

References

Anderson, M. P., and Woessner, W. W. (1992). Applied groundwater modeling simulation of flow and advective transport. Academic Press, Inc., New York. Bear, J. (1972). Dynamics offluids in porous media. Elsevier, New York. Bear, J., and Verruijt, A. (1987). Modeling groundwater flow and pollution. Reidel Publishing Co., Holland. Beljin, M. S. (1988). "Testing and validation of models for simulating solute transport in groundwater," GWMI 88-11, International Groundwater Modeling Center, Golden, CO. (1991). "SOLUTE: A program package for analytical models for solute transport in groundwater," (computer program), IGWMCBAS 15, Version 2.03, International Ground Water Modeling Center, Golden, CO. Brooks, R. H., and Corey, A. T. (1964). "Hydraulic properties of porous media," Hydrology Paper No. 3, Colorado State University, Fort Collins, CO. Campbell, G. S. (1974). "A simple method for determining unsaturated conductivity from moisture retention data," Soil Science 117(6), 311314. Celia, M. A., Gray, W. G., and Hassanizadeh, S. M. (1992). "Validation of Geo-hydrological models," Advances in Water Resources 15, Part 2. Faust, C. R., and Mercer, J. W. (1980). "Groundwater modeling: Recent developments," Groundwater 18(6), 569-577. Fetter, C. W. (1993). Contaminant hydrogeology. Macmillan Publishing Company, New York. Geraghty and Miller (1992). "Groundwater modeling survey: Analysis of May 1992 survey results," Geraghty and Miller Modeling Group, Reston, VA.

References

131

Goode, D. J., and Konikow, L. F. (1989). "Modification of a methodof-characteristics solute-transport model to incorporate decay and equilibrium-controlled sorption or ion exchange," USGS-WRI Report 89-4030, U.S. Geological Survey. Hadala, P. F., Butler, D. K., Cullinane, M. J., Holland, J. P., May, I., and McDaniel, T. (1993). "Army groundwater modeling use and needs workshop," Technical Report IRRP-93-1, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS. Haverkamp, R., Vauclin, M., Touma, J., Wierenga, P. J., and Vachaud, G. (1977). "A comparison of numerical simulation models for onedimensional infiltration," Soil Science Society of America Journal 41, 285-294. Hill, M. C. (1990). "Preconditioned Conjugate-Gradient 2 (PCG2), A computer program for solving groundwater flow equations," Water Resources Investigations Report 90-4048, U.S. Geological Survey, Denver, CO. Hossain, M. A., and Corapcioglu, M. Y. (1985). "Modifying the USGS solute transport computer model to predict high-density hydrocarbon migration," Ground Water 26(6), 717-723. Huyakorn, P. S., and Nilkuha, K. (1978). "Solution of transient transport equation using an upstream weighted finite element scheme," Applied Mathematical Modeling 3, 3-17. Huyakorn, P. S., and Pinder, G. F. (1983). Computational methods in subsurface flow. Academic Press, Inc., San Diego, CA. Kaluarachchi, J. J., and J.C. Parker (1989). "An efficient finite element method for modeling multiphase flow in porous media," Water Resources Research 25(1), 43-54. (1990). "Modeling multicomponent organic chemical transport in three fluid phase porous media," Journal of Contaminant Hydrology 5, 349-374. Katyal, A. K., Kaluarachchi, J. J., and Parker, J. C. (1991). MOFAT: A two-dimensional finite element program for multiphase flow and multicomponent transport - Program documentation and user's guide. EPA/600/2-91/020 (PB91-191692). Katyal, A. K., and Parker, J. C. (1992). "An adaptive solution domain algorithm for solving multiphase flow equations," Computers and Geosciences 18(1), 1-9. Khanji, D. J. (1975). "Study of free-surface water layers by infiltration," M.S. thesis, University of Grenoble, France.

132

References

Kincaid, C. T., and Morrey, J. R. (1984). "Geochemical models for solute migration, Volume 2: Preliminary evaluation of selected computer codes," EA-3417, Electric Power Research Institute. Konikow, L. F., and Bredehoeft, J. D. (1978). "Computer model of twodimensional solute transport and dispersion in ground water," Techniques of water-resources investigations of the United States Geological Survey. Bk. 7, Chapter C2. . (1992). "Groundwater models cannot be validated," Advances in Water Resources 15, 75-83. Lappala, E. G., Healy, R. W, and Weeks, E. P. (1987). "Documentation of computer program VS2D to solve the equations of fluid flow in variably saturated porous media," USGS, Water-Resources Investigations Report 83-4099. Lyman, W. J., Reehl, W. F., and Rosenblatt, D. H. (1982). Handbook of chemical property estimation methods. McGraw-Hill, New York. Maidment, D. R. (1993). Handbook of hydrology. McGraw-Hill, Inc., New York. Mangold, D. C, and Tsang, C. F. (1991). "A summary of subsurface hydrological and hydrochemical models," Review of Geophysics 29(1), 51-79. McDonald, M. G., and Harbaugh, A. W. (1984). "A modular threedimensional finite-difference ground-water flow model," U.S. Geological Survey Open File Report 83-875, U.S. Geological Survey. . (1988). "A modular three-dimensional finite-difference ground-water flow model." Techniques of water resources investigations of the United States Geologica Survey. Book 6, Chapter Al. McDonald, M. G., Harbaugh, A. W., Orr, B. R., and Ackerman, D. J. (1991). "A method of converting no-flow cells to variable-head cells for the U.S. Geological Survey modular finite-difference ground-water flow model," Open-File Report 91-536, U.S. Geological Survey, Washington, DC McWhorter, D. B., and Sunada, D. K. (1977). Ground-water hydrology and hydraulics. Water Resources Publications, Littleton, CO. Mercer, J. W., and Cohen, R. M. (1990). "A review of immiscible fluids in the subsurface: Properties, models, characterization, and remediation," Journal of Contaminant Hydrology 6, 107-163. Millington, R. J., and Quirk, J. P. (1959). "Gas diffusion in porous media," Science 130, 100-102.

References

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Mishra, S., Parker, J. C, and Singhai, N. (1989). "Estimation of soil hydraulic properties and their uncertainty from particle size distribution data," Jour. Hydrology 108, 1-18. Montgomery, J. H. (1991). Groundwater chemicals desk reference Volume 2. Lewis Publishers, Inc., MI. Montgomery, J. H., and Welkom, L. M. (1989). Groundwater chemicals desk reference. Lewis Publishers, Inc., MI. Morrey, J. ., Kincaid, C. T., and Hostetler, C. J. (1986). "Geohydrochemical models for solute migration; Volume 3: Evaluation of selected computer codes," EA-3417, Volume 3, Electric Power Research Institute. Moskowitz, P. D., Pardi, R., DePhillips, M. P., and Meinhold, A. F. (1992). "Computer models used to support cleanup decision-making at hazardous and radioactive waste sites," Broookhaven National Laboratory, Long Island, New York. Nofziger, D. L., Rajender, K., Nayudu, S. K, and Su, P. Y. (1989). "CHEMFLO one dimensional water and chemical movement in unsaturated soils," EPA/600/8-89/076, Robert S. Kerr Environmental Research Laboratory, U.S. Environmental Protection Agency, Ada, OK OSWER. (1989). "OSWER models study: Promoting appropiate use of models in hazardous waste/superfund programs, Phase I final report," IMS, Office of Solid Waste and Emergency Response, U.S. Environmental Protection Agency, Washington, DC. . (1990). "Report on the usage of computer models in hazardous waste/superfund programs, Phase II final report," IMS, Office of Solid Waste and Emergency Response, U.S. Environmental Protection Agency, Washington, DC. Pinder, G. F. (1973). "A Galerkin-finite element simulation of groundwater contamination on Long Island, New York," Water Resources Research 9(6), 1657-1669. Prickett, T. A., and Lonnquist, C. G. (1971). "Selected digital computer techniques for groundwater resource evaluation," Bulletin 55, Illinois State Water Survey, Urbana, IL. Prickett, T. A., Naymik, T. G., and Lonnquist, C. G. (1981a). "A 'RANDOM-WALK' solute transport model for selected groundwater quality evaluations," Illinois State Water Survey, Bulletin 65, Champaign, IL. (1981b). "A 'RANDOM-WALK' solute transport model for selected groundwater quality evaluations," IGWMC Software FOS 13 PC, Illinois State Water Survey, Champaign, IL.

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References

Prill, R. C, Johnson, A. I., and Morris, D. A. (1965). "Specific yieldlaboratory experiments showing the effect of the time on column drainage," USGS Water Supply Paper 1662-B, U.S. Geological Survey. Prudic, D. E. (1989). "Documentation of a computer program to simulate stream-aquifer relations using a modular, finite-difference, groundwater flow model," Open-File Report 88-729. U.S. Geological Survey, Carson City, NV. Rifai, H. S., Bedient, P. B., Borden, R. C, and Haasbeek, J. F. (1987). BIOPLUMEII - Computer model of two-dimensional contaminant transport under the influence of oxygen limited biodegradation in ground water. User's Manual - Ver. 1.0. Sanford, W. E., and Konikow, L. F. (1985). "A two-constituent solutetransport model for ground water having variable density," USGS Water-Resources Investigations Report 85-4279, U.S. Geological Survey. van der Heijde, P. K. M., and Elnawawy, O. A. (1992). "Quality assurance and quality control in the development and application of groundwater models," Robert S. Kerr Environmenatl Research Laboratory, U.S. Environmental Protection Agency, Ada, OK. van Genuchten, M. Th. (1978). "Calculating the unsaturated hydraulic conductivity with a new, closed-form analytical model," Research Report 78-WR-08, Water Resources Program, Department of Civil Engineering, Princeton University, Princeton, NJ. (1980). "A closed-form equation for predicting the hydraulic conductivity of unsaturated soils," Soil Science Society of America Journal 44, 892-898. Vauclin, M., Khanji, D. J., and Vachaud, F. (1979). "Experimental and numerical study of a transient, two-dimensional unsaturated-saturated water table recharge problem," Water Resources Research 15(5), 10891101. Voss, C. I. (1984). "A finite-element simulation model for saturatedunsaturated, fluid-density-dependent groundwater flow with energy transport or chemically reactive single-species solute transport," USGS Water Resources Investigations Report 84-4369, Reston, VA. Wagner, J., and Ruiz-Calzada, C. E. (1987). "Evaluation of models for unsaturated-saturated flow and transport," Robert S. Kerr Environmental Research Laboratory, U.S. Environmental Protection Agency, Ada, OK. Wagner, J., Watts, S. A., and Kent, D. C. (1984). "PLUME 2D twodimensional plumes in uniform groundwater flow," Robert S. Kerr Environmental Research Laboratory, U.S. Environmental Protection Agency, Ada, OK.

References

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Walton, W. C. (1989). Numerical groundwater modeling: Flow and contaminant modeling. Lewis Publishers, Chelsea, MI. Whisler, F. D., and Watson, K. K. (1968). "One-dimensional gravity drainage of uniform columns of porous materials." Wilson, J. L., and Miller, P. J. (1978). Two-dimensional plume in uniform groundwater flow," Journal of the Hydraulics Division, ASCE, 104(HY4), 503-514. Yeh, G. T., and Cheng, J. R. (1994). "User's manual: A three-dimensional finite element model of water flow through saturated-unsaturated media: Version 2.0," Department of Civil Engineering, Pennsylvania State University, University Park, PA. Zheng, C. (1988). "New solution and model for evaluation of groundwater pollution control," Ph.D. diss., University of Wisconsin-Madison. . (1990). "MT3D: A modular three-dimensional model for the simulation of advection," Prepared for the U.S. Environmental Protection Agency. . (1992). "MT3D: A modular three-dimensional transport model, Version 1.5, Documentation and user's guide," second revision, S. S. Papdopulos and Associates, Inc., Bethesda, MD. . (1993). "Extension of the method of characteristics for simulation of solute transport in three dimensions," Groundwater 31(3), 456-465.

136

References



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